Comparator:-

• A comparator is a combinational circuit used to compare two binary numbers.

2-bit Comparator:-

• 2-bit Comparator is a combinational circuit used to compare two binary number consiting of two bits. When two binary numbers A & B are compared the output can be any of these three cases i.e. A > B, A = B and A < B.
• To design any combinational circuit we have to follow the steps given below.

1. Construct the truth table for the given problem.
2. Derive the boolean expressions for the required outputs.
3. Simplify the boolean expressions if necessary.
4. Construct the combinational circuit.

• Construct the truth table for the given problem.

* Derive the boolean expressions for the required outputs.

The boolean equations are simplified by using K-Map

$When \ A = B \ then \\Y = \overline A_1\ \overline A_0\ \overline B_1\ \overline B_0+ \overline A_1\ A_0\ \overline B_1\ B_0+ A_1\ A_0\ \ B_1\ B_0 + A_1\ \overline A_0\ B_1\ \overline B_0 \\ = \overline A_1\ \overline B_1( \overline A_0\ \overline B_0\ + A_0\ B_0)+A_1\ B_1( \overline A_0\ \overline B_0\ + A_0\ B_0) \\ = ( \overline A_1\ \overline B_1\ + A_1\ B_1) \cdot ( \overline A_0\ \overline B_0\ + A_0\ B_0)$

• Simplify the boolean expressions if necessary.

The equations are simplified by using K-Map.

• Construct the combinational circuit.

The circuit for A > B is as follows

The circuit for A = B is as follows