COMPARATORS

• It is a combinational circuit which compares the two numbers and determines their relative magnitude
• The output of comparator is generally 3 binary variables indicating: A>B

A=B

A<B

• For instance to design a comparator for two bit binary numbers A (A1A0) and B (B1B0) we perform the following steps:

1-bit comparator: Let's start with one bit comparator and from the name we can easily make out that it circuit would be used to compare one bit binary numbers.

If we list all input combinations at input then we get the table describing the corresponding outputs which is stated as follows.

A             B             f (A>B)  f (A=B) f (A<B)

Further we find the equations by using K-maps each for f (A>B), f (A=B) and f (A<B) as shown below:

• For a two-bit comparator we have 4 inputs A₁A₀ and B₁B₀ and 3 output E ( is 1 if 2 numbers are equal) G (is 1 when A > B) and L (is 1 when A < B) If we use the truth table and KMAP the result is given by
• E= A’₁A'₀B’₁B’₀ + A’₁A₀B _’ 1B₀ + A₁A₀B₁B₀ + A₁A _’ 0B₁B’₀

or E=(( A₀ ⊕B₀) + ( A₁ ⊕B₁))’

G = A₁B’₁ + A₀B'₁B'₀ + A₁A₀B'₀

L= A'₁B₁ + A'₁A'₀B₀ + A'₀B₁B₀

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