(a) Show how two 2-to-1 multiplexers (with no added gates) could be connected to form a 3-to-1 MUX. Input selection should be as follows: If AB = 00, select I0 If AB = 01, select I1 If AB = 1− (B is a don’t-care), select I2 (b) Show how two 4-to-1 and one 2-to-1 multiplexers could be connected to form an 8-to-1 MUX with three control inputs. (c) Show how four 2-to-1 and one 4-to-1 multiplexers could be connected to form an 8-to-1 MUX with three control inputs

Explanation:

a) Show how two 2-to-1 multiplexers (with no added gates) could be connected to form a 3-to-1 MUX. Input selection should be as follows: If AB = 00, select I0 If AB = 01, select I1 If AB = 1− (B is a don’t-care), select I2

We are to show how Two-2-to -1 multiplexers could be connected to form 3-to-1 MUX

If AB = 00 select

If AB = 01 select

If AB = 1_(B is don't care), select

However, the truth table is attached and shown in the first file below.

Also, the free- body diagram for 2- to - 1 MUX is shown in the second diagram attached below.

b) We are show how  two 4-to-1 and one 2-to-1 multiplexers could be connected to form an 8-to-1 MUX with three control inputs.

The perfect illustration showing how they are connected in displayed in the third free-body diagram attached below.

Where ; are the inputs of the multiplexer and Z is the output.

c)  Show how four 2-to-1 and one 4-to-1 multiplexers could be connected to form an 8-to-1 MUX with three control inputs.

For  four 2-to-1 and one 4-to-1 multiplexers could be connected to form an 8-to-1 MUX with three control inputs, we have a perfect illustration of the diagram in the last( which is the fourth) diagram attached below.

Where ; are the inputs of the multiplexer and Z is the output