Question

A combinational circuit has four inputs A, B, C, and D representing the 16 binary integers from 0 to 15. A is the most significant bit and D is the least significant bit. The output of the circuit F is true (logic 1)if the input is exactly divisible by a multiple of 4, 5, 6, or 7 with the exception of 15, in which case the output is false (logic 0). Zero is not divisible by 4, 5, 6, or 7.

Complete the truth table AND the corresponding K- MAP for the circuit AND give the simplified Boolean expression for the circuit.

Answer 1

To create the truth table for the combinational circuit, consider all possible inputs and use the given conditions to determine the output. Use the divisibility rules to determine if the output is true or false. The simplified Boolean expression can be obtained by analyzing the truth table.

Step-by-step explanation:

In order to create the truth table for the given combinational circuit, we need to consider all possible inputs (A, B, C, D) and determine the corresponding output (F). Since there are 4 inputs, there will be 2^4 = 16 possible input combinations.

We can use the given conditions to determine whether the output is true or false. The output is true (logic 1) if the input is exactly divisible by a multiple of 4, 5, 6, or 7, with the exception of 15. Zero is not divisible by any of these numbers. Therefore, we need to check if each input is divisible by any of these numbers and determine the output accordingly.

We can fill in the truth table by checking each possible input combination and determining the output based on the divisibility rules. The simplified Boolean expression can be obtained by analyzing the truth table and identifying common patterns.