**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. A_{3}B_{3} is 10 and A_{2}A_{1}A_{0 }& B_{2}B_{1}B_{0} can be anything:

A=1xxx, B=0xxx

2. A_{3}=B_{3 }and A_{2}B_{2} is 10 and A_{1}A_{0} & B_{1}B_{0} can be

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

3. A_{3}=B_{3} and A_{2}=B_{2} and A_{1}B_{1}=10 and A_{0}B_{0} 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}=A_{3}B_{3}’+S_{3}A_{2}B_{2}’+S_{3}S_{2}A_{1}B_{1}’+S_{3}S_{2}S_{1}A_{0}B_{0}’**

**Logic ****For A < B**

For A < B, there are also 4 cases:

1) A_{3}B_{3 }is 01 and A_{2}A_{1}A_{0} & B_{2}B_{1}B_{0 }can be anything:

1. A=0xxx, B=1xxx

2) A_{3}=B_{3 }and A_{2}B_{2} is 01 and A_{1}A_{0} & B_{1}B_{0} can be

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

3) A_{3}=B_{3} and A_{2}=B_{2} and A_{1}B_{1}=01 and A_{0}B_{0} 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}=A_{3 }’B_{3}+S_{3}A_{2 }’B_{2}+S_{3}S_{2}A_{1 }’ B_{1}+S_{3}S_{2}S_{1}A_{0 }’ B_{0}**

**4-bit Comparator Logic Circuit**

**MSI: 7485 4-bit Magnitude Comparator**

**Comparison of 4-bit Numbers**

**Comparison of 8 - bit Numbers**

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