Question

Implement a four-input majority function using a 4-to-1 multiplex. The 4-input majority function is a function from four inputs to one output. The value of the operation is zero when two or more arguments are zero. Otherwise, the function outputs one. You need to draw the schematics of your design and write down the intermediate steps.

Answer 1

The four-input majority function can be implemented using a 4-to-1 multiplexer as follows:

Define the truth table for the four-input majority function:

A B C D Output

0 0 0 0 0

0 0 0 1 0

0 0 1 0 0

0 0 1 1 1

0 1 0 0 0

0 1 0 1 1

0 1 1 0 1

0 1 1 1 1

1 0 0 0 0

1 0 0 1 1

1 0 1 0 1

1 0 1 1 1

1 1 0 0 1

1 1 0 1 1

1 1 1 0 1

1 1 1 1 1

A 4-to-1 multiplexer with the data inputs (A, B, C, D) is made

Each data input (A, B, C, D) is assigned to the multiplexer's output

A: Connect to the output of a 2-to-1 multiplexer that selects between B and D based on S0.

B: Connect to the output of a 2-to-1 multiplexer that selects between C and D based on S1.

C: Connect to the output of a NOT gate inverting the value of A.

D: Connect to a constant value of 1.

Connect the control inputs of the multiplexer to the control signals derived from the truth table:

S0: Connect to the output of an AND gate that takes the inputs A and B.

S1: Connect to the output of an AND gate that takes the inputs A and NOT(C).

The output of the 4-to-1 multiplexer represents the output of the four-input majority function.