Here we’ll be designing circuits to compare different binary numbers. Suppose we have two numbers A & B at the input and 3 output as A>B, A=B, A<B and only one of the three outputs would be high accordingly if A is greater than or equal to or less than B.
1-bit comparator: Let’s begin with 1 bit comparator and from the name we can easily make out that this circuit would be used to compare 1 bit binary numbers. If we list all the input combinations at the input then we get the following table describing the corresponding outputs.
A B f (A>B) f (A=B) f (A<B)
0 0 0 1 0
1 0 1 0 0
0 1 0 0 1
1 1 0 1 0
And now we find the equations using K-maps each for f (A>B), f (A=B) and f (A<B) as follow: