Subtractor/Multiplier Section 4.5 & 4.7
Jan 07, 2016
Subtractor/Multiplier
Section 4.5 & 4.7
Outline
• Delay • Four Bit Subtractor• Multiplier
Four Bit Adder
Erroneous Results When Delay is inserted in half_adder.v
Four-Bit Adder
C4 is calculated last because it takes C0 8 gates to reach C4.Each FA uses 2 XOR, 2 AND and 1 OR gate.A four-bit adder uses 8 XOR, 8 AND and 4 OR gate.
Build a Full-Adder Circuit
w1
w2 w3
M1 M2
One gate-delay
Wait for the four bit adder circuit to compute the results
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Subtraction
Unsigned Number
Decimal b1 b0
0 0 0
1 0 1
2 1 0
3 1 1
(2-bit example)
Unsigned Addition
• 1+2=
Decimal b1 b0
0 0 0
1 0 1
2 1 0
3 1 1
Decimal b1 b0
1 0 1
+ 2 1 0
3 1 1
Unsigned Addition
• 1+3=
Decimal b1 b0
0 0 0
1 0 1
2 1 0
3 1 1
Decimal b1
b0
1 1
1 0 1
+ 3 1 1
4 1 0 0
(Carry Out)
(Indicates Overflow)
Overflow can be an issue in unsigned addition.
Unsigned Subtraction (1)
• 1-2=
Decimal b1 b0
0 0 0
1 0 1
2 1 0
3 1 1
Decimal b1
b0
1 0 1
+ -2 1 0
1 1
0 0
-1 0 1
(1’s complement)
(2’s complement)
Unsigned Subtraction (2)
• 2-1=
Decimal b1 b0
0 0 0
1 0 1
2 1 0
3 1 1
Decimal b1 b0
1
2 1 0
+ -1 1 1
3 1 0 1
Discarded
Summary for Unsigned Addition/Subtraction
• Overflow can be an issue in unsigned addition (An overflow is detected from the end carry out of the most significant position)
• Unsigned Subtraction (M-N)– If M≥N, and end carry will be produced.
The end carry is discarded.– If M<N, • Take the 2’s complement of the sum• Place a negative sign in front
Four-Bit Adder-Subtractor
For detecting overflow in addition/subtraction of signed numbers
For detecting overflow in unsigned numbers
The Mode Input (1)
B0
If M=0, = If M=1, =
The Mode Input (2)
If M=0, If M=1,
M=0 (Addition)
0
B3 B2 B1 B0
M=1 (Subtraction)
1
2’s complement is generated of B is generated!
Four-Bit Adder-Subtractor
FA0FA1FA2FA3
X0X1X2X3
X4
X_FA_0X_FA_1X_FA_2X_FA_3
Verilog Model of a 4 bit adder/subtractor
Sample output of adder/subtractor circuit
Ignore V if you are working with unsigned numbers.
Binary Multiplication
Two-Bit Binary Multiplier
(multiplicand)
(multiplier)
𝐴 0𝐵00 0 0
0 1 0
1 0 0
1 1 1
Use an AND gate to multiply A0 and B0
Hardware Correlation
Hardware Correlation
G0G1
G2G3
W0W1W2
W3
HA1 HA0