Data Representation and Digital Logic - Assignment 1

IT COMPUTER
Name of the Student
Student ID
Subject Code (ITC544)
Assignment 1: Data Representation and Digital Logic
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IT COMPUTER
Question 1
Answer (a): Firstly, let covert hexadecimal Number (6A) to equivalent decimal
number.
⇒ (6A) 16
= (6) (161) + (10) (160)
= 96 + 10
= 106
(152)x = (6A)16
So we can conclude:-
(152) x = 106
(1) (X2) + (5) (x1) + (2) (x0) = 106
X2 + 5x + 2 = 106
X2 + 5x+ 104 = 0
The value of x is 8 (Answer)
Answer (b):
I. 0xBED is a number with radix 16. in hexadecimal number (B), (E) and (D)
represent following (11), (14) and (13).
The decimal representation of the 0xBED is:
⇒ (11) (162) + (14) (161) + (13) (160)
= 2816 + 224 + 13
= 3053
= (3053)10
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IT COMPUTER
Now, let (3053)10 convert into base 3 number:
=3053
3 3053 2
3 1017 0
3 339 0
3 113 2
3 37 1
3 12 0
3 4 1
3 1
So, (3053)10 = (11012002)3
II. convert (321)7 into 2-base (binary)
First,
Let (321)7 convert to (x)10.
(3) (72) + (2) (71) + (1) (70)
= 162
= (162)10
Now let converting (162)10 to (x)2
2/162⇔81 – remainder 0
2/81 ⇔ 40 – remainder 1
2/40⇔20 – remainder 0
2/20⇔10 – remainder 0
2/10⇔5 – remainder 0
2/5 ⇔ 2 – remainder 1
2/2⇔1 – remainder 0
The answer is: (321)7 = (10100010)2
III. 1235 into octal representation:
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