P$3(20$ points$)$: $1-$t$0-8$ demultiplexer

a$)$ Write the Boolean functions for the outputs of a $1-$to$-8$ demultiplexer

that an $$nput F with select lines IA$,$ B$,$ CI$.$

b$)$ Implement the demultiplexer using AND, and NOT gates.

c$)$ Implement the demultiplexer using $1-$to$-2$ demultiplexers and a

minimal number Of additional gate$$

d$)$ Implement the multiplexer using $1-$t$0-4$ demultiplexers and a minimal

number of additional gatesP$3(20$ points$)$: $1-$t$0-8$ demultiplexer

a$)$ Write the Boolean functions for the outputs of a $1-$to$-8$ demultiplexer

that an $$nput F with select lines IA$,$ B$,$ CI$.$

b$)$ Implement the demultiplexer using AND, and NOT gates.

c$)$ Implement the demultiplexer using $1-$to$-2$ demultiplexers and a

minimal number Of additional gate$$

d$)$ Implement the multiplexer using $1-$t$0-4$ demultiplexers and a minimal

number of additional gates