Assignment

Complete the following in a paper of 1-2 pages:

1. Simplify the following Boolean expression: AB(A + B)(C + C)

2. Design the combinatorial circuit for: (p' *r) + q

3. Design the combinatorial circuit for: [(p^q') V (r V q)] /\s

4. Complete the truth table of the following Boolean expression: p'/\(q V r)

5. Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for your proof, or complete the two truth tables:

o (A + C)(AD + AD') + AC + C
o A + C

6. The following is a message coded in ASCII using one byte per character and then represented in hexadecimal notation. What is the message?

o 4469736372657465204D617468656D617469637320697320434F4F4C21

7. Convert each of the following signed binary byte representations to its equivalent base-ten representation. What would each byte represent in Binary Coded Decimal? Show your work step by step.

o 00010001
o 01011100
o 1111010 What is the signed binary sum of 1011100 and 1110101 in decimal? Show all of your work.

8. Convert each of the following base-ten representations to its equivalent two's complement in 7 bits. Show all of your work.

o 12
o -2
o -8
o 0

o Define the highest and lowest integer that can be represented in this 7-bit two's complement representation.

9. What bit patterns are represented by the following hexadecimal notations? Show all of your work.

o 9A88
o 4AF6
o DA

o What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work.