Logic Circuits and Digital Design
Combinational Circuit & Boolean Simplification
Design a circuit such that it will output 1, if the sum of the number’s decimal digits is 5 or 7. The input is 5-bit numbers.
For instance, if the input is 14 or 25 the sum is 1 + 4 = 5 and 2 + 5 = 7, therefore the output is 1. For instance, if the input is 17, the sum is 1 + 7 = 8 so the output is 0.
a. First draw the truth table for this problem.
b. Then write down the Boolean expression for the output where each row is represented as a product term in sum of products form.
c. Then simplify the resultant Boolean expression. During simplification you have to use one XNOR gate where A XNOR B = A’B’ + AB.
d. Design your resultant simplified circuit using Logisim.
e. Simulate your resultant circuit to be sure it works flawless.
