1. Perform the following Octal addition directly, without converting to another base.
667 + 213
2. Perform the following Hexadecimal addition directly, without converting to another base.
1 0 6 6 + A B C D
3. Given a list of numbers num[0], num[1], ..., num[N], write an algorithm in pseudo code to find the Minimum value in the list.
4. Briefly explain what Abstraction means. Give two examples (not the erroneous one in the text).
5. What is the lowest base in which 605 would be a valid number?
6. If 11110010 is in 2's complement notation, what signed decimal number does it represent?
7. Convert the decimal number 5.73 to binary. Stop after 4 decimal places. Show your work.
8. Complete the following table. Each row is the same number written in different bases. Each column is the same base. All values are positive.
|
Binary
|
Octal
|
Decimal
|
Hexadecimal
|
|
01100111
|
|
|
|
|
|
|
53
|
|
|
|
342
|
|
|
9. Show the behavior of the following circuit by completing the given truth table with the Boolean Expressions and the corresponding truth values
|
A
|
B
|
C
|
|
|
|
|
0
|
0
|
0
|
|
|
|
|
0
|
0
|
1
|
|
|
|
|
0
|
1
|
0
|
|
|
|
|
0
|
1
|
1
|
|
|
|
|
1
|
0
|
0
|
|
|
|
|
1
|
0
|
1
|
|
|
|
|
1
|
1
|
0
|
|
|
|
|
1
|
1
|
1
|
|
|
|
Boolean Identities
|
Property
|
AND
|
OR
|
|
Commutative
|
AB = BA
|
A + B = B + A
|
|
Associative
|
(AB)C = A(BC)
|
(A + B) + C = A + (B + C)
|
|
Distributive
|
A(B + C) = (AB) + (AC)
|
A + (BC) = (A + B)(A + C)
|
|
Identity
|
A1 = A
|
A + 0 = A
|
|
Complement
|
A(A') = 0
|
A + (A') = 1
|
|
DeMorgan's Law
|
(AB)' = A' + B'
|
(A + B)' = A'B'
|
|
Idempotent
|
AA = A
|
A + A = A
|
|
Boundedness
|
A0 = 0
|
A + 1 = 1
|
|
Involution
|
(A')' = A
|
|
A' means NOT A
10. Simplify the Boolean Expression C(AC)' + BC'A' . Show all the steps.
|
Character
|
Huffman Code
|
|
Character
|
Huffman Code
|
|
A
|
00
|
|
O
|
10010
|
|
E
|
11
|
|
I
|
10011
|
|
T
|
010
|
|
N
|
101000
|
|
C
|
0110
|
|
F
|
101001
|
|
L
|
0111
|
|
H
|
101010
|
|
S
|
1000
|
|
D
|
101011
|
|
R
|
1011
|
|
|
|
11. a) What word does the following bit sequence represent?
10100100101000010001000010100110110
b) How many bits would it take to represent the word from part a) using ASCII characters assuming that one would use 8 bits per ASCII character?
c) What is the compression ratio between parts a) and b)?
d) Translate the following hexadecimal sequence into English
48 65 78 61 64 65 63 69 6D 61 6C
12. A. Consider the following "Super Simple CPU" program. Does it have a Loop? If it does, circle (or write down) the code that causes a Loop.
B. Trace the code and determine what the final values in Mem[11] (memory location 11), Mem[12], and Mem[13] will be after the program has executed. The original values are given.
TOP LOD 12
SUB 11
JZR XX
JNG YY
STO 12
JMP TOP
XX LDI 1
STO 13
STP
YY STO 13
STP
11 DAT 3
12 DAT 9
|
|
Accumulator
|
Mem[11]
|
Mem[12]
|
Mem[13]
|
|
Original values
|
0
|
3
|
9
|
0
|
|
Final values
|
|
|
|
|
What would be in Mem[13] if the original value of Mem[12] was 8.
13. Consider the following truth table for a circuit where A, B, C are the input and X is the sole output.
|
A
|
B
|
C
|
X
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
0
|
0
|
|
1
|
0
|
0
|
0
|
|
0
|
1
|
1
|
0
|
|
1
|
0
|
1
|
1
|
|
1
|
1
|
0
|
1
|
|
1
|
1
|
1
|
1
|
a) Give a Boolean expression for the circuit and simplify if possible.
b) Draw a circuit implementing this expression using standard logic gate symbols.
14. Describe Two Methods to determine if two distinct circuits are equivalent?
15. The Greek alphabet has 25 symbols. How many bits would be required to represent the Greek alphabet?
Attachment:- Assignment.rar