Applications of Discrete Mathematics and Statistics in IT
Jerrica
itco341_ip1.docxComplete 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 Λ q’) V ( r V q)] Λ s
4. Complete the truth table of the following Boolean expression: p’ Λ (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:
· (A + C)(AD + AD’) + AC + C
· 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?
· 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.
· 00010001
· 01011100
· 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.
· 12
· -2
· -8
· 0
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.
· 9A88
· 4AF6
· DA
What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work.
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 Λ q’) V
( r V q)] Λ s
4.
Complete the truth table of the following Boolean expression: p’ Λ (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 binar
y 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
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
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 Λ q’) V ( r V q)] Λ s
4. Complete the truth table of the following Boolean expression: p’ Λ (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
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
