Need help to slove those questions * Simplify the following Boolean expressions using algebraic manipulation.

Note: You must show all the steps with explanation (laws used) to get the full point. Solutions without the intermediate steps will not be accepted.

Note that ' means -not- (i.e., the same as a bar over a variable or expression)

Example: F(a,b) = b+(ab)'

Solution:

b+(ab)'

b+(a'+b') DeMorgan's Law

(b+b')+a') Commutative, Associative Laws

1+ a' Complement Law

1 Identity Law

a. F(a,b) = (b'+ a)(a + b) b. F(r,s,t) = rs'+r(s+t)'+s(s+t)'

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

* Design a simple combinational circuit which calculates the result of the function F(n) = 5n + 3, where n is any 2-bit unsigned integer. In designing the circuit, draw a truth table, derive expressions for each of the outputs, and draw the circuit. You must show the process. You should not need a K-map. You must use Logisim to draw the circuit.