Transcript Subtractor/Multiplier

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
M1
M2
w1
w2
One gate-delay
w3
Wait for the four bit adder circuit
to compute the results
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ENGINEER III – AIRCRAFT ELECTRONICS
SUMMARY
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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=
(Indicates Overflow)
Decimal
b1
b0
0
0
0
1
0
1
2
1
0
3
1
1
Decimal
b
1
b
0
1 1
+
1
0
1
3
1
1
4
1 0
0
(Carry Out)
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
b
1
b
0
1
0
1
-2
1
0
1
1
0
0
(1’s complement)
0
1
(2’s complement)
-1
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
1 0
1
3
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 unsigned
numbers
For detecting overflow in addition/subtraction of signed numbers
The Mode Input (1)
If M=0, 𝐵0 ⊕ 0= 𝐵0
If M=1, 𝐵0 ⊕ 1= 𝐵0
B0⊕ 𝑀
The Mode Input (2)
If M=0, C0 = 0
If M=1, C0 = 1
M=0 (Addition)
B3
B2
B1
B0
0
M=1 (Subtraction)
𝐵3
𝐵2
𝐵1
𝐵0
1
2’s complement is generated of B is generated!
Four-Bit Adder-Subtractor
X2
X3
X_FA_2
X_FA_3
FA3
X4
X_FA_1
FA2
X0
X1
X_FA_0
FA1
FA0
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)
𝐴0𝐵0
𝐴0
B0
𝐴0𝐵0
0
0
0
0
1
0
1
0
0
1
1
1
Use an AND gate to multiply A0 and B0
Hardware Correlation
Hardware Correlation
G1
G3
W3
HA1
G0
G2
W2
W1
W0
HA0