3 Boolean Algebra and Implementation

i. Simplify each of the following two Boolean equations.

ii. Sketch a reasonably simple combinational circuit implementing the simplied equation.

iii. Compare the numbers of literals and operators versus the numbers of gates, nets, and pins in the schematic diagrams

A. abc + abd + abcd + bcd + acd + abcd + acd

B. (a+b+c+d)(a+b+c+d)(a+b+c)(a +b+c+d)(a +c+d)(a +b+c +d)

4 From Problem to Boolean Expression

A majority voting machine inputs ve binary bits (x_4,x₃,x₂,x₁,x₀), and outputs y = 1 when the majority of the input bits are 1. Otherwise, the output is y = 0.

i. Write the truth table.

ii. Write the functions in sum-of-products canonical form.

iii. Write the functions in product-of-sums canonical form.