Design a combinational circuit with three inputs, $x,y$ and $z,$ and three outputs, $A,B,C.$ When the binary

input is $0,1,2,$ or $3,$ the binary output is one greater than the input. When the binary input is $4,5,6,$ or $7,$

the binary output is two less than the input.

A majority circuit is a combinational circuit whose output is equal to $1$ if the input variables have more

$1\text{'}$s than $0\text{'}$s$.$ The output is $0$ otherwise. Design a $3-$input majority circuit by finding the circuit's truth table,

Boolean equation, and a logic diagram.

Design a BCD$-$to$-$decimal decoder using the unused combinations of the BCD code as don't$-$care

conditions.

Construct a $5-$to$-32-$line decoder with four $3-$to$-8-$line decoders with enable and a $2-$to$-4-$line decoder.

Using a decoder and external gates, design the combinational circuit defined by the following three

Boolean functions:

a$)F1=x^{\text{'}}yz{z}^{\text{'}}+xz$

b$)$

c$)F2=x{y}^{\text{'}}{z}^{\text{'}}+x^{\text{'}}x$

d$)$ F$2=y^{\text{'}}{z}^{\text{'}}+x^{\text{'}}y+x{z}^{\text{'}}$

e$)F3=x^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}+xy$