Question

I need to implement the gates on Logism, please clearly explain all steps.

Part A: Design and wire a circuit to implement the Boolean expression S (x, y, z) = ∑m (1, 2, 4, 7) usingan 8-to-1 multiplexer . Verify the operation by checking all input combinations in the Boolean function's truth table.

Part B: Implement the function S (x, y, z) from Part A using only a 4-to-1 multiplexer .You may use NOT gates as needed.

Part C: Implement the function in Part A using a decoder (your variables are used as input and you can use an OR gate after your decoder).

Answer 1

SOLUTION -

PART - A

Given minterms = 1, 2, 4, 7

Implementing the given function using 8x1 mux

the function has 3 variables and mux has 3 selection lines so give 3 variables to 3 selection lines

and according to given min terms place the values in the 8 pins

Truth table:

logic circuit using 8x1 mux

S0,S1,S2 are selection lines

PART -B

implementing S using 4x1 mux here we have 3 variables and our mux has 2 selection lines

so taking one variable as external variable and giving inputs based on that variable Z

Truth table

Logic diagram:

PART - C

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