Question

Design A Combinational Circuit That Compares Two Four Bit Numbers To Check If They Are Equal. The Circuit Output Should Equal 1 If The Two Numbers Are Equal And 0 Otherwise. [Hint: The Exclusive NOR Is The Equivalence Function]

Design a combinational circuit that compares two four bit numbers to check if they are equal. The circuit output should equal 1 if the two numbers are equal and 0 otherwise.

[hint: the exclusive NOR is the equivalence function]

Answer 1

To design a combinational circuit that compares two four-bit numbers and checks if they are equal, use the Exclusive NOR (XNOR) gate with four gates comparing the corresponding bits of the numbers.

Step-by-step explanation:

To design a combinational circuit that compares two four-bit numbers and checks if they are equal, we can use the Exclusive NOR (XNOR) gate, which is the equivalence function. The circuit should have four XNOR gates, each comparing the corresponding bits of the two numbers.

For example, let's compare the numbers A = 1101 and B = 1011:

• A: 1 1 0 1
• B: 1 0 1 1XOR or XNOR
• Output: 0 1 0 1

If the output is 1, it means the numbers are equal. If the output is 0, it means the numbers are not equal.

Therefore, the combinational circuit can be implemented using four XNOR gates, with each gate comparing the corresponding bits of the two numbers.