Design a combinational circuit with three inputs $(x,y,z)$ and one output $(5)$ where

a$)$ The output is $1$ when the binary value of the inputs is less than $2.$ The output is $0$ otherwise.

b$)$ The output is $1$ when the binary value of the inputs is less than $3.$ The output is $0$ otherwise.

c$).$ The output is $1$ when the binary value of the inputs is less than $5.$ The output is $0$ otherwise.

d$)$ The output is $1$ when the binary value of the inputs is less than $6.$ The output is $0$ otherwise.

Answer:

$A=F=x^{\text{'}}y{z}^{\text{'}}+x{y}^{\text{'}}{z}^{\text{'}}+xy{z}^{\text{'}}$

$B=F=x^{\text{'}}y{z}^{\text{'}}+x{y}^{\text{'}}{z}^{\text{'}}+xy{z}^{\text{'}}+xyz$

$C=F=x^{\text{'}}y{z}^{\text{'}}+x{y}^{\text{'}}{z}^{\text{'}}+xy{z}^{\text{'}}+xyz+xy{z}^{\text{'}}$

$D=F=x^{\text{'}}y{z}^{\text{'}}+x{y}^{\text{'}}{z}^{\text{'}}+xy{z}^{\text{'}}+xy{z}^{\text{'}}+xy{z}^{\text{'}}+xyz$