Chapter 1 - Review

Digital Computersand Information

Chapter 1

Mano and Kime

Digital Computersand Information

• Digital Computers

• Number Systems

• Arithmetic Operations

• Decimal Codes

• Error Detection and Correction

Block Diagram of Computer

Memory

• ROMs and PROMs

• EPROMs, EEPROMs and Flash Memory

• Static RAMs and Dynamic RAMs

ROMs and PROMs

• ROM– Read-Only Memory

• PROM– Programmable Read-Only Memory

EPROMs, EEPROMs and Flash Memory

• EPROM– Erasable Programmable Read-Only Memory– Erase with ultraviolet light

• EEPROM– Electrically-Erasable Programmable Read-Only

Memory

• Flash Memory– Electrically-Erasable in bulk

RAMs• RAM

– Random-Access Memory– Read-Write Memory

• Static RAM– Needs 4 transistors per bit to make a latch– Data lost when power is turned off

• Dynamic RAM– One transistor per bit– Data stored as charge on a capacitor– Data must be continually refreshed

W8XMicrocontroller

mux4g

F C R M

Reg_Array

(mux2g)

ALU

N1

(stack8x16)rpoprpushReturn Stack

(mux2g)

(mux2g)

P reg

I Reg

Controller(w8x_control)

ProgramROM

P mux

R muxT mux

(reg)

(incrg)

R

M

TN

T

p_in

t_in

alu_out mux_out

alu_sel mux_sel

I

T

P

P1

iload

pload

pinc

tsel

rsel

psel

r_in

M

cregCout

C

M

T

sel0sel1sel2sel3

load

clr

clk

clk

clr

clr

clk

clk

clr

plus1P1

clr clkcload

Control UnitDatapath

The W8Z Microprocessor

reg_stack

Funit

TN2 N1N3

d0

y1cout

clr

clk

Rcode(3:0)

Fcode(4:0)

msel(5:0)

Wcontrol

Wrom

WPC

clk

clr

inc

M(15:8)M(7:0)

P

d1

ReturnStack

R

Pmux

Rmux

dual_mux8g

add2

sub1

ROM

RAM

T

T N1

y2

SW(1:8)

rsel(1:0)

psel

BTN(1:4)

rpush

rload

pselrsel

pload

DigReg

LDreg

dig3 dig1dig4 dig2

LD(1:8)

T

TN1

clrclk

rpush

rpop

pload

clrclk

rload

rdecclkclr

we

rpoprdec

ldloadclk

clr

clk

clr digload

P1

R

R1

RM1

p_in

r_in

T

T

Mmuxcnt1

clk clr

tog

c1

instr

tog

inc

ldload we

Digital Computerand Information

• Digital Computers

• Number Systems

• Arithmetic Operations

• Decimal Codes

• Error Detection and Correction

Powers of 2

Numbers with Different Bases

Number Systems

N = ...P3P2P1P0 . P-1P-2P-3...

= ... + P3b3 + P2b2 + P1b1 + P0b0

+ P-1b-1 + P-2b-2 + P-3b-3 + ...

375.1710 = 3 x 102 + 7 x 101 + 5 x 100

+ 1 x 10-1 + 7 x 10-2 = 300 + 70 + 5 + 0.1 + 0.07= 375.17

Number Systems

N = ...P3P2P1P0 . P-1P-2P-3...

= ... + P3b3 + P2b2 + P1b1 + P0b0

+ P-1b-1 + P-2b-2 + P-3b-3 + ...

1101.112 = 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 + 1 x 2-1 + 1 x 2-2

= 8 + 4 + 0 + 1 + 1/2 + 1/4= 13.7510

Binary

Number Systems

N = ...P3P2P1P0 . P-1P-2P-3...

= ... + P3b3 + P2b2 + P1b1 + P0b0

+ P-1b-1 + P-2b-2 + P-3b-3 + ...

1AB.616 = 1 x 162 + A x 161 + B x 160

+ 6 x 16-1 = 1 x 256 + 10 x 16 + 11 x 1 + 6/16 = 256 + 160 + 11 + 0.375 = 427.37510

Hex

Number Systems

N = ...P3P2P1P0 . P-1P-2P-3...

= ... + P3b3 + P2b2 + P1b1 + P0b0

+ P-1b-1 + P-2b-2 + P-3b-3 + ...

173.258 = 1 x 82 + 7 x 81 + 3 x 80

+ 2 x 8-1 + 5 x 8-2

= 1 x 64 + 7 x 8 + 3 x 1+ 2/8 + 5/64

= 64 + 56 + 3 + 0.25 + 0.078125= 123.32812510

Octal

Examples

Convert the following binary numbers to decimal:

1101001

10001011.011

10011010

Digital Computerand Information

• Digital Computers

• Number Systems

• Arithmetic Operations

• Decimal Codes

• Error Detection and Correction

Recall Full Adder Truth Table

0 0 0 0 00 0 1 1 00 1 0 1 00 1 1 0 11 0 0 1 01 0 1 0 11 1 0 0 11 1 1 1 1

Ci Ai Bi Si Ci+1

00 1 0 10 1 1 1

A

B

0

1

0

1

1

1

1

C

Final carry = 0

Binary Addition

0 0 1 1 0 1 0 10 0 0 1 1 0 0 1 0111

0

0

1

0

53+25 78

35+19 4E

Dec Hex

Binary

1001

1

0

0

Number System Conversions

• Hex, Binary, and Octal to Decimal

• Binary Hex

• Binary Octal

• Hex Octal

• Decimal to Hex, Octal, and Binary

Hex to Decimal8 7 C 9

x 16 128 + 7 135 x 16 2,160 + 12 2,172 x 1634,752 + 934,761

Binary Hex

0110 1010 1000 . 1111 0101 1100

6 A 8 . F 5 C

Binary Octal

011 010 101 000 . 111 101 011 100

3 2 5 0 . 7 5 3 4

Hex OctalGo through Binary

0110 1010 1000 . 1111 0101 1100

6 A 8 . F 5 C

011 010 101 000 . 111 101 011 100

3 2 5 0 . 7 5 3 4

Convert Decimal to any BaseInteger Part: Divide by the base,keep track of the remainder, and read up.

16 34,761 16 2,172 rem 9 16 135 rem 12 = C 16 8 rem 7 0 rem 8

Read up

34,76110 = 87C916

Convert Decimal to any Base

Fractional Part: Multiply by the base, keep track of the integer part, and read down.

0.78125 x 16 = 12.5 int = 12 = C

0.5 x 16 = 8.0 int = 8

Readdown

0.7812510 = 0.C816

Convert Decimal to any Base

Fractional Part: Multiply by the base, keep track of the integer part, and read down.0.1 x 2 = 0.2 int = 00.2 x 2 = 0.4 int = 00.4 x 2 = 0.8 int = 00.8 x 2 = 1.6 int = 10.6 x 2 = 1.2 int = 10.2 x 2 = 0.4 int = 00.4 x 2 = 0.8 int = 0

Readdown

0.110 = 0.000112

ExamplesConvert the following numbers from the given base to the other three bases listed in the table:

F3C7.A???

?326.5??

??10111101.101?

???369.3125

HexOctalBinaryDecimal

Binary Coded Decimal

Code decimal numbers using the binary digits, 0 - 9.That is, 0000 - 1001.Can NOT use the hex digits A - F.For example, the DECIMAL number 3582 wouldbe coded in BCD as

0011 0101 1000 0010While this looks like the HEX number 3582Hin BCD we interpret it as the DECIMAL number 3582.

BCD Addition

Binary

35H 00110101+47H 01000111 7CH 01111100

Decimal (BCD)

35H 00110101+47H 01000111 82H 10000010

0000 B0 35 MOV AL,35H ;AL = 35H0002 04 47 ADD AL,47H ;AL = AL+47H0004 27 DAA ;Decimal adjust

Digital Computerand Information

• Digital Computers

• Number Systems

• Arithmetic Operations

• Decimal Codes

• Error Detection and Correction

Error Detection and Correction

• Use of Parity Bit

- Extra bit included to make the total number of 1’s either even or odd. Refer to page : 22 for an example.

* If a parity error is detected at the receiving end, it can request for a retransmission.

More topics…

• Fixed and Floating point numbers – Refer to the ppt presentation on the course website.