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Explore the design of a two-bit binary multiplier using AND gates for multiplicands A0 and B0. This section covers hardware correlation, discussing outputs G0-G3 based on inputs W[0]-W[3]. Understand the workings of a four-bit by three-bit binary multiplier, defining computations such as S10=A0B1+A1B0 and others. Additionally, learn how to implement a magnitude comparison circuit to establish equality (A=B), greater than (A>B), or less than (A<B) among binary numbers A and B. The importance of significant bits in determining relationships is crucial in these operations.
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Binary MultiplicationMagnitude Comparison Section 4.5, 4.7 and 4.8
Two-Bit Binary Multiplier (multiplicand) (multiplier)
Hardware Correlation G1 G0 G3 G2 W[2] W[0] W[1] W[3]
Four-bit by three-bit Binary Multiplier S10=A0B1+A1B0 S11=A0B2+A1B1+C11 S12=A0B3+A1B2+C12 S13=0+A1B3+C13 (S1X/C1X, where 1 is the first 4-bit adder)
Magnitude Comparison • Given A and B where • A=A3A2A1A0 • B=B3B2B1B0 • Three possibilities: • A=B • A>B • A<B
A=B • A=B, if all pairs of significant digits are equal • A3=B3 • A2=B2 • A1=B1 • A0=B0 • Each pair can be equal if they are either 0s or 1s • Xi=AiBi+A’iB’i
Equality Check • Xi=AiBi+A’iB’i (Identical?) ==(+)(+B0)=+++0=+ 0
A>B • Start from the most significant bit • A=1*** >B=0*** • Work toward less significant bits • A=11**>B=10**
Interpretation x3 can only be a 1 if A3=B3. x2 can only be a 1 if A2=B2. X1 can only be a 1 if A1=B1. 1 if A3 =1 and B3=0 Interpretation: 1 is only possible if A3=B3 and A2=1 and B2=0. Comments: If any of the terms gives rise to a 1 A>B.
A>B A>B
