A+ Work

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 Λ q’) V ( r V q)] Λ s

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

5.                         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

6.                         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.

7.                         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

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

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

o                           9A88

o                           4AF6

o                           DA

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