Question

Show a comparator that can compare two 2 - bit binary numbers with help of a logic diagram, and write the corresponding Boolean expressions, and truth table.

Answer 1

2-BIT COMPARATOR

Let's consider we have two 2-bit binary numbers i.e., A1A0 and B1B0.

Login circuit diagram:

Boolean expressions:

K-map for L (A < B):

L (A < B) = ~A1 ~A0 B0 + ~A1 B1 + ~A0 B1 B0

K-map for E (A = B):

E (A = B) = ~A1 ~A0 ~B1 ~B0 + ~A1 A0 ~B1 B0 + A1 ~A0 B1 ~B0 + A1 A0 B1 B0

K-map for G (A > B):

G (A > B) = A0 ~B1 ~B0 + A1 ~B1 + A1 A0 ~B0

Truth table:

In the above circuit and truth table:

• L represents A < B
• E represents A = B
• G represents A > B