1. Simplify the following Boolean expressions using algebraic manipulation.

a. F(a,b) = ab + ab + ab'

b. F(r,s,t) = r + rt + rs + rst

c. F(x,y) = (x + y)(x + y)

d. F(a,b,c) = b'+ bc + ab + a'bc'

e. F(a,b,c,d) = ac + b'd + a'bc + b'cd'

Note that means not (i.e. a bar over a variable or expression)

2. Design a simple combinational circuit which calculates the result of the function F(n) = 5n + 4, where n is any 2bit unsigned integer. In designing the circuit, draw a truth table, derive expressions for each of the outputs, and draw the circuit. You may use boolean algebra for simplification (i.e. no Kmaps).