Note: For simplicity in writing in problems 4, 5 and 6, the expression A.B is denoted by AB.

1. Convert the following numbers to the required representations for each of the following decimal numbers? Show the necessary steps.

a) 234710 = ( )2

b) 9872110 = ( )8

c) 58210 = ( )16

d) 13.62510 = ( )2 - Extra credit: Investigate how to convert fractions from decimal to

binary.

2. Perform the arithmetic operations below. Use 7-bit signed-2s complementrepresentation (including sign bit). In each case, determine if there is an overflow. Show the necessary steps. a) 35+40

b) 35-40 c) -35 - 40

3. Simplify the following Boolean expression and write a truth table for the simplified equation.

a) AB+BC(B+C)

b) A + B(A + C) + AC

4. Convert the expression (BC + D)(C + AD ) into the following.

a) SOP

b) POS

5. Express the function F (A, B, C, D) = AC + BD + BC + BD as the following.

a) sum of minterms

b) product of maxterms

(Note: you may want to simplify this).

6. Implement the following Boolean functions

a) F(w, x, y, z) = ?(2, 3, 5, 6, 11, 14, 15) using 8:1 multiplexer

b) F(w, x, y, z) = ?(2, 3, 5, 6, 11, 14, 15) using just NOR gates