2-Bit Magnitude Comparator

Compares two 2-bit numbers A (A1A0) and B (B1B0), outputting which is greater or if equal. IC reference: 74HC85.

2-Bit Comparator — IC 74HC85

GROUP A GROUP B 74HC85 COMPARATOR 2-BIT MAGNITUDE A1 A0 B1 B0 A>B A=B A<B GROUP A 0 A1 0 A0 GROUP B 0 B1 0 B0 A>B 0 A=B 0 A<B 0
A 00 = 0
=
B 00 = 0
A = B

Truth Table (all 16 combinations)

AB A>B A=B A<B
0 (00) 0 (00) 0 1 0
0 (00) 1 (01) 0 0 1
0 (00) 2 (10) 0 0 1
0 (00) 3 (11) 0 0 1
1 (01) 0 (00) 1 0 0
1 (01) 1 (01) 0 1 0
1 (01) 2 (10) 0 0 1
1 (01) 3 (11) 0 0 1
2 (10) 0 (00) 1 0 0
2 (10) 1 (01) 1 0 0
2 (10) 2 (10) 0 1 0
2 (10) 3 (11) 0 0 1
3 (11) 0 (00) 1 0 0
3 (11) 1 (01) 1 0 0
3 (11) 2 (10) 1 0 0
3 (11) 3 (11) 0 1 0

How the Comparator Works

A > B

A1·B̄1 + EQ1·A0·B̄0

A1>B1, OR bits are equal and A0>B0

A = B

XNOR(A1,B1) · XNOR(A0,B0)

All bits are equal (XNOR → 1 when inputs match)

A < B

Ā1·B1 + EQ1·Ā0·B0

Symmetric to A>B — A1<B1, or equal high bits and A0<B0

Key property

Exactly one output is always HIGH. GT + EQ + LT = 1 for all input combinations.