How to solve Multiplexer problems from given sum of min-terms

A  MUX (Multiplex) is a data selecting device which selects an input and transfers it to the Output with the help of select inputs. Here several data can be transmitted through the same channel and minimizes the required bandwidth of the channel.

Relation between Select Inputs and no. of Inputs : I=2^s

Where I= Number of MUX Inputs

And S= Number of select Inputs

Example: If number of Inputs is 8 then s=3 as 2³=8

Problem: Design a 8:1 MUX Circuit from the given function f=∑ (1, 5, 6, 7, 10, 11, 14)

Solution:

Rule 1:  Column with one circled element will get the respective row value.

                Example: element 1 is circled and will get the respective row value A’ (A complement).

Rule 2: Column with no circled element will get a zero value and it will be grounded.

                Example: column I₀

Rule 3: Column with two circled elements will get value 1

                Example: Column I₆

MUX Circuit Representation: