Chapter No.5
DATA REPRESENTATION
Q.5.01 Complete the following statements.
i) Data is a collection of ________________
ii) Data becomes information when ________________ properly.
iii) Octal equivalent of binary number 1100010 is________________
iv) 2’s complement of binary number 1100010 is ________________
v) In floating point representation, mantises is kept less than________________
vi) ASCII stands for ________________________________
Ans:
i) raw facts
ii) arranged
iii) 142
iv) 0011110
v) 1
iv) American Standard Code for Information Interchange
Q.5.02 Which of the following statements are True or False?
i) PK 345 is an example of Alphabetic data.
ii) 128 is not an octal number.
iii) In hexadecimal number F is equivalent to 16 in decimal number.
iv) EBCDIC code is used in IBM compatible computers.
v) Binary Coded Decimal (BCD) is a 10-bit code.
Ans:
i) False
ii) True
iii) False
iv) True
v) False
Q.5.03 Encircle one Choice A, B, C or D I each case
i) Binary coded decimal (BCD) express each decimal digit as:
(A) Binary digit (B) Byte
(C) Nibble
(D) Word
ii) The number 1000 comes immediately after:
(A) 900
(B) FFF
(C) 887
(D) 499
iii) The radix of a computerized version of the number (+0.66 E – 4) is:
(A) 2
(B) 4
(C) 6
(D) 8
iv) The number of possible combinations in a 7-bit code are:
(A) 49
(B) 64
(C) 128
(D) 256
v) Which of the following is a 16-bit code?
(A) BCD
(B) Unicode (C) ASCII
(D) EBCDIC
Ans:
i) (A)
ii) (C)
iii) (A)
iv) (C)
v) (B)
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Q.5.04 Match the items given in Column I with those given in Column II
i)
ii)
iii)
iv)
v)
Column I
Mantissa
Radix
Exponent
BCD
ASCII
Column II
a)
b)
c)
d)
e)
Nibble
Byte
Argument
Base
Characteristics
Ans:
i) (c)
ii) (d)
iii) (e)
iv) (a)
v) (b)
Q.5.06 Describe the importance of binary number system in computers.
Ans: The importance of binary numbers in standard computing is basically everything.
Computers only understand base 2 that is a 0 (off) and a 1 (on). Every piece of data
passed through any part of the computer is done so using base 2 (binary).
Q.5.07 Convert the following decimal numbers into their binary equivalent.
(i) 47
(ii) 167
(iii) 0.875
(iv) 21.625
Above questions are same as the following example.
Example: Convert Decimal number 25.75 into Binary equivalent.
Solution:
2
25
0.75 X 2
= 1.5
2
12
0.5 X 2
= 1.0
2
6
2
3
1
Hence
(25.75)10 = (11001.11)2
Q.5.08 Convert the following binary numbers into their decimal equivalent.
(i) 101101
(ii) 1001110
(iii) 0.10111
2
(iv) 101.0101
Above questions are same as the following example.
Example: Convert Binary number 10110.101 into decimal equivalent.
Solution:
(10110.101)2
= 1 X 24 + 0 X 23 + 1 X 22 + 1 X 21 + 0 X 20 + 1 X 2-1 + 0 X 2-2 + 1 X 2-3
= 1 X 16 + 0 X 8 + 1 X 4 + 1 X 2 + 0 X 1 + +
= 16 + 0 + 4 + 2 + 0 + 0.5 +
+
+
= 22.5 + 0 + 0.125
= 22.625
= (22.625)10
Q.5.09 Convert the following decimal numbers into their octal equivalent.
(i) 43
(ii) 291
(iii) 168
(iv) 2101
Above questions are same as the following example.
Example: Convert Decimal number 1583 into Octal equivalent.
Solution:
8
1583
8
197
8
24
3
Hence
(1583)10 = (3057)8
Q.5.10 Convert the following octal numbers into their decimal equivalent.
(i) 27
(iii) 372
(iii) 1101
Above questions are same as the following example.
Example: Convert octal number 3057 into decimal equivalent.
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(iv) 2345
Solution:
(3057)8 = 3 X 83 + 0 X 82 + 5 X 81 + 7 X 80
= 3 X 512 + 0 X 64 + 5 X 8 + 7 X 1
= 1536 + 0 + 40 + 7
= 1583
= (1583)10
Q.5.11 Convert the following decimal numbers into their Hexadecimal equivalent.
(i) 37
(iii) 141
(iii) 532
(iv) 702
Above questions are same as the following example.
Example: Convert Decimal number 20154 into Hexadecimal equivalent.
Solution:
16
20154
16
1259
=A
16
78
=B
4
=E
Hence
(20154)10 = (4EBA)16
Q.5.12 Convert the following Hexadecimal numbers into their decimal equivalent.
(i) 4F
(iii) BA4C
(iii) 532
Above questions are same as the following example.
Example: Convert Hexadecimal number 3F8A into decimal equivalent.
Solution:
(3F8A)16
= 3 X 163 + F X 162 + 8 X 161 + A X 160
= 3 X 4096 + 15 X 256 + 8 X 16 + 10 X 1
= 12288 + 3840 + 128 + 10
= 16266
= (16266)10
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(iv) 702
Q.5.13 Subtract:
(i) 10102 from 11012
(ii) 1010012 from 1101102
(iii) 11112 from 101012
(iv) 100012 from 111002
(v) 10102 from 10010012
Ans:
using 1’s and 2’s complement
for part (i) to (iv)
Above questions from (i) to (iv) are same as the following example.
Example:
1010
- 1101
----------------------0011
----------------------part (v) is same as the following example:
Example: Subtract (1101)2 from (10010)2 in binary system using 1’s and 2’s complement
method.
1’s Complement Method:
1st make equal digits in both the numbers by adding 0’s on the left. Like following
Making equal digits of Binary numbers: 01101 and
1’s complement of 01101
=
10010
10010
10010
Adding 1’s complement of 01101
+
10010
1 00100
Adding the carry
+
1
00101
Thus (10010)2 – (1101) 2 = (101) 2
2’s Complement Method:
1st make equal digits in both the numbers by adding 0’s on the left. Like following
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Making equal digits of Binary numbers: 01101 and
1’s complement of 01101
=
10010
2’s complement of 01101
=
10010+1
=
10011
10010
10010
Adding 2’s complement of 01101
+
10011
1 00101
Dropping the carry
00101
Thus (10010)2 – (1101) 2 = (101) 2
Q.5.14 What is meant by coding in computers?
Ans: Coding is the process of representing all the numeric or non-numeric information in binary digits.
The language of electronic computers is binary therefore all the numeric or non-numeric data
must be converted in to binary language.
Q.5.15 Describe ASCII code and EBCDIC code?
The ASCII Code
ASCII stands for American Standard Code for Information Interchange. It is 7-bit code used to handle
alphanumeric data having 128 different characters. It is the most popular coding system for PC’s and
data communication. This code allows manufactures to standardize input/output devices such as
keyboard, printers visual display unit etc.
The EBCDIC Code
EBCDIC stands for Extended Binary Coded Decimal Interchange Code. It an 8-bit code and can provide
256 different characters. It is primarily used by International Business Machine on IBM mainframes and
on other large computers.
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