Data Representation and Digital Logic: Conversion and Circuit Analysis

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ITC544
ASSIGNMENT 1: DATA REPRESENTATION AND DIGITAL LOGIC)

Question 1
a) (152)x = (6A)16
x = ?
6A is in hexadecimal, the decimal representation will be
6 * 161 + 10 * 160
= 96 + 10
= 106 in decimal
152 is with base x, the decimal representation will be
1 * x2 + 5 * x1 + 2 * x0
x2 + 5x + 2 in decimal
Therefore, x2 + 5x + 2 = 106
x2 + 5x – 104 = 0
x2 + 13x – 8x – 104 = 0
(x + 13)(x – 8) = 0
x = 8, x = -13
As the value of base cannot be negative.
Therefore x = 8.
b)
i) 0xBED into 3-base representation
BED is in hexadecimal, the decimal representation is:
11 * 162 + 14 * 161 + 13 * 160
= 2816 + 224 + 13
= 3053
Now, 3053 is converted to base 3
3 3053 2
3 1017 0
3 339 0
3 113 2
3 37 1
3 12 0
3 4 1
3 1 1
0
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[WRITE YOUR FULL NAME]
[WRITE YOUR STUDENT ID]
ITC544
ASSIGNMENT 1: DATA REPRESENTATION AND DIGITAL LOGIC)

Now, these remainders are written upside down, therefore,
0xBED = (11012002)3
ii) (321)7 into 2-base (binary) representation
321 is in base 7, the decimal representation is:
3 * 72 + 2 * 71 + 1 * 70
= 147 + 14 + 1
= 162
Now, 162 is converted to binary
2 162 0
2 81 1
2 40 0
2 20 0
2 10 0
2 5 1
2 2 0
2 1 1
0
Now, these remainders are written upside, therefore,
(321)7 = (10100010)2
iii) (123)5 into octal representation
123 is in base 5, the decimal representation is:
1 * 52 + 2 * 51 + 3 * 50
= 25 + 10 + 3
= 38
Now, 38 is converted to base 8
8 38 6
8 4 4
0
Now, these remainders are written upside down, therefore,
(123)5 = (46)8
iv) (21.21)8 into decimal representation
2 * 81 + 1 * 80 + 2 * 8-1 + 1 * 8-2
= 16 +1+ 0.25+0.015625
= (17.265625)10
c)
i) One’s complement
Lowest value (negative)  011
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