Digital Logic Circuits–Comparator

Comparator

Comparator compares binary numbers.

Logic comparing 2 bits: a and b

Magnitude Comparator

Comparator compares binary numbers

4-bit Magnitude Comparator:

Inputs: A3A2A1A0 & B3B2B1B0

Outputs: Y _A>B, Y _A<B, Y _A=B

For each bit, let:

Si = AiBi + Ai’Bi’ = (AiBi’ + Ai’Bi)’

Si is true when Ai = Bi

For A = B, we must have:

A3=B3 and A2=B2 and A1=B1 and A0=B0

Hence, Y _A=B = S3•S2•S1•S0 136

Logic For A > B

For A > B, there are 4 cases:

1. A₃B₃ is 10 and A₂A₁A₀ & B₂B₁B₀ can be anything:

A=1xxx, B=0xxx

2. A₃=B₃ and A₂B₂ is 10 and A₁A₀ & B₁B₀ can be

anything: A=11xx, B=10xx or A=01xx, B=00xx

3. A₃=B₃ and A₂=B₂ and A₁B₁=10 and A₀B₀ is xx: e.g.

A=011x, B=010x

4. A3=B3 and A2=B2 and A1=B1 and A0B0 is 10: e.g.

A=1011, B=1010

Y _A>B=A₃B₃’+S₃A₂B₂’+S₃S₂A₁B₁’+S₃S₂S₁A₀B₀’

Logic For A < B

For A < B, there are also 4 cases:

1) A₃B₃ is 01 and A₂A₁A₀ & B₂B₁B₀ can be anything:

1. A=0xxx, B=1xxx

2) A₃=B₃ and A₂B₂ is 01 and A₁A₀ & B₁B₀ can be

1. anything: A=10xx, B=11xx or A=00xx, B=01xx

3) A₃=B₃ and A₂=B₂ and A₁B₁=01 and A₀B₀ is xx: e.g.

1. A=110x, B=111x

4) A3=B3 and A2=B2 and A1=B1 and A0B0 is 01: e.g.

1. A=1000, B=1001

Y _A<B=A₃ ’B₃+S₃A₂ ’B₂+S₃S₂A₁ ’ B₁+S₃S₂S₁A₀ ’ B₀

4-bit Comparator Logic Circuit

MSI: 7485 4-bit Magnitude Comparator

Comparison of 4-bit Numbers

Comparison of 8 - bit Numbers