Similarly we can have 2 bit comparator and the table to list all the combinations at input and their corresponding outputs is as:
A B f (A>B) f (A=B) f (A<B)
00 00 0 1 0
01 00 1 0 0
10 00 1 0 0
11 00 1 0 0
00 01 0 0 1
01 01 0 1 0
10 01 1 0 0
11 01 1 0 0
00 10 0 0 1
01 10 0 0 1
10 10 0 1 0
11 10 1 0 0
00 11 0 0 1
01 11 0 0 1
10 11 0 0 1
11 11 0 1 0
And we get the equations for all three outputs from the K-maps as
We can also obtain these equations orally as for A1A0 to be greater than B1B0 either A1 is greater than B1 (i.e. A1=1 & B1=0) or A1 is equal to B1 (or A1is not less than B1 i.e. (f(A1<B1))’ = (A1’B1)’= (A1 + B1‘) & A0 is greater than B0 (i.e. A0=1 & B0=0).
Hence the equation we get is f (A>B) = A1B1‘+ (A1 + B1’) A0B0’ = A1B1‘+ A0 B1’B0’+ A1A0B0’
We can also get the equation orally similar to the above case. Now we can implement the above equation easily. Similarly we can implement other higher comparators