Shannon decomposition William Sandqvist william@kth.se Claude Shannon mathematician / electrical engineer (1916 –2001) William Sandqvist william@kth.se.

Shannon decomposition

William Sandqvist williamkthse

Claude Shannon mathematician electrical engineer (1916 ndash2001)

William Sandqvist williamkthse (Degital Design Ex4)

(Ex 86)Show how a 4-to-1 multiplexer can be used as afunction generator for example to generate theOR function

Multiplexer as function generator

(Ex 86)

Show how a 4-to-1 multiplexer can be used as afunction generator for example to generate theOR function

BV 61Show how the function

can be implemented using a 3-to-8 decoder and an OR gate

)754320()( 321 mwwwf

A majority gate outputs the same value as the majority of the inputs The gate can for example be used in fault-tolerant logic or in image processing circuits a) (Set up the gates truth table and minimize the function with Karnaugh map Realize the function with AND-OR gates )

b) Realize the majority gate with an 8 1 MUX

c) Use Shannon decomposition and realize the majority gate with a2 1 MUX and gates

d) Realize the majority gate with only 21 MUXes

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

With 8-to-1 mux hellip

Shannon decomposition 2-to-1 mux and gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

Shannon decomposition Only 2-to-1 muxes

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

use Shannonrsquos expansion to derive an implementation using a 2-to-1 multiplexer and any necessary gates

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

Show how one four-input exorgate (XOR odd parity function) is realized in an FPGA circuit Show the contents of the SRAM cells ( LUT Lookup Table )

(Ex 88)

Set up full adder truth table Show how a full adder is implemented in an FPGA chip Logic elements of an FPGA is able to cascade COUT and CIN between neighbors Show the contents of the SRAM cells ( LUT Lookup Table )

(BV ex 631)In digital systems it is often necessary to have circuits that can shift the bits of a vector one or more bit positions to the left or right Design a circuit that can shift a four-bit vector W = w3w2w1w0 one bit position to the right when a control signal Shift is equal to 1 Let the outputs of the circuit be a four-bit vector Y = y3y2y1y0 and a signal k such that if Shift = 1 then y3 = 0 y2 = w3 y1 = w2 y0 = w1 and k = w0 If Shift = 0 then Y = W and k = 0

We uses MUXes

(BV ex 631)

(BV ex 631)We uses MUXes

BV ex 632Barrel shifter

The shifter in Example 631 shifts the bits of an input vector by one bit position to the right It fills the vacated bit on the left side with 0 If the bits that are shifted out are placed into the vacated position on the left then the circuit effectively rotates the bits of the input vector by a specified number of bit positions Such a circuit is called a barrel shifter

Design a four-bit barrel shifter that rotates the bits by 0 1 2 or 3 bit positions as determined by the valuation of two control signals s1 and s0

A barrelshifter is used to speed up floating point operations

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

Key Benefits Lowest FPGA unit cost starting at $049 Ultra-low power in FlashFreeze mode as low as 2 microW Nonvolatile FPGA eliminates unnecessary parts from BOM Single-chip and ultra-low-power products simplify board design Variety of cost-optimized packages reduce assembly costs Low-power FPGAs reduce thermal management and cooling needs

BV 616

Actel Corporation manufactures an FPGA family called Act 1 which uses multiplexer based logic blocks Show how the function

can be implemented using only ACT 1 logic blocks

323132 wwwwwwf

BV 616323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

VHDL BV 251aWrite VHDL code to describe the following functions

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL code is written with a text editor and saved in a file with the extensionvhd The code always consists of two sections ENTITY and ARCHITECTURE

Entity is a description of how the circuit looks from the outside (the interface) and Architecture how it looks like inside

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

Comments begin with ndash-If you wish you can draw clarification ASCII graphics in the comment lines

-- ___________ -- | |-- | Functions |-- -gt-| x1 |-- -gt-| x2 f1 |-gt--- -gt-| x3 f2 |-gt--- -gt-| x4 |-- |___________|--

Program code is written with a text editor So we can only do text comments to the code A fixed-width font is used( eg Courier New )

One usually indent text blocks that belong together for greater clarity

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

ENTITY Functions IS PORT(x1 x2 x3 x4 IN STD_LOGIC f1 f2 OUT STD_LOGIC )END Functions

ARCHITECTURE LogicFunc OF Functions ISBEGIN f1 lt= (x1 AND NOT x3)OR(x2 AND NOT x3)OR (NOT x3 AND NOT x4)OR(x1 AND x2)OR (x1 AND NOT x4) f2 lt= (x1 OR NOT x3)AND(x1 OR x2 OR NOT x4)AND (x2 OR NOT x3 OR NOT x4) END LogicFunc

VHDL BV 621

Using a selected signal assignement write VHDL code for a 4-to-2 binary encoder Only one of w0 hellipw3 is rdquo1rdquo at a time

LIBRARY ieeeUSE IEEEstd_logic_1164allENTITY ENCODER IS PORT( w IN STD_LOGIC_VECTOR( 3 DOWNTO 0 ) y OUT STD_LOGIC_VECTOR( 1 DOWNTO 0 ) )END ENCODERARCHITECTURE Behavior OF ENCODER ISBEGIN WITH w SELECT y lt= rdquo00rdquo WHEN rdquo0001rdquo rdquo01rdquo WHEN rdquo0010rdquo rdquo10rdquo WHEN rdquo0100rdquo rdquo11rdquo WHEN OTHERSEND Behavior

(810) Additional if time permits

0233010102 xxxxxxxxxxY

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

Or if you donrsquot have acess to the variable x0 inverted hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

BV ex 632 Barrel shifter

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 86)

)754320()( 321 mwwwf

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 86)

)754320()( 321 mwwwf

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 86)

)754320()( 321 mwwwf

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)754320()( 321 mwwwf

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)754320()( 321 mwwwf

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)754320()( 321 mwwwf

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

With AND OR gates

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

bcabacM

With AND OR gates

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

bcabacM

With AND OR gates

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()( bccbcbabca

abccabcbabcaM

OR)()( cbabca

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1)1()(

0)()0(

bcbcbcbbcbcbcbbbcbh

cbbcbbg

cbhbcgcbacbaM

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

For the function

)6320()( 321 mwwwf

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

For the function

)6320()( 321 mwwwf

)110011010000()(

321321

3213232321

321321321321

wwwwww

wwwwwwwwww

wwwwwwwwwwww

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 89)

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 88)

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

We uses MUXes

(BV ex 631)

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

Barrel shifter

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

BV ex 632

Truth table

W0W1W2W3

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

BV ex 632

Truth table

W0W1W2W3

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

BV ex 632

And so on

Truth table

W0W1W2W3

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

= Lowcost FPGA

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

BV 616

323132 wwwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1223223

122312123

21212322213213

)10()(

wwwwwwwf

wwwwwwwww

wwwwwwwwwwwwww

wwwwwf

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

VHDL BV 251a

)()()( 432421312

41214332311

xxxxxxxxf

xxxxxxxxxxf

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

023 xxx

301 xxx

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

1 1 - -

3 2 (00)x x

3 2 (01)x x

3 2 (11)x x

3 2 (10)x x

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

23 )00(

23 )10(

23 )11(

23 )01(

0x0x0x

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(00)x x

23 )10(

23 )11(

(10)x x

Or hellip

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

(Ex 86)

(Ex 89)

(Ex 88)

(BV ex 631)

Barrel shifter

BV ex 632

= Lowcost FPGA

BV 616

VHDL BV 251a

VHDL BV 621

Shannon decomposition William Sandqvist william@kth.se Claude Shannon mathematician / electrical engineer (1916 –2001) William Sandqvist william@kth.se.

degital design ex48

degital design ex4ex

degital design ex4bv

gateswilliam sandqvist

mux william sandqvist

c shannon decomposition

majority gate outputs

c use shannon decomposition

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