Sreedhar’s CCE

COMPUTER AWARENESS-6
Number System

Various number systems

1. Decimal Number System Base 10 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

2. Binary System Base 2 0 and 2
3. Octal System Base 8 0, 1, 2, 3, 4, 5, 6, 7
4. Hexa Decimal System Base 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
A, B, C, D, E, F

Note: Octal System is a 3-bit representation of the digits used i.e. 23=8; Hexadecimal
system is a 4-bit representation of the digits used i.e. 24=16.

Various coding Schemas are-

1. BCD: It is a 16-bit code (26=64).

2. ASCII: It is a 7-bit code (27=128)
3. EBCDIC: It is a 8-bit code (28=256)

Difference between bit and Byte

Bit: It is the smallest unit of storage measurement. It represents a 0 or 1 binary digit.

It is used in representing small memories.
Byte: It is a combination of 8 bits used as a unit for storing data. It represents an
alphabet, character or special symbol. It is used to represent large memories. A Byte can
represent a decimal equivalent value of up to 256 different values.

Fixed Point:

In this system all numbers are represent as Integers or Fractions.

The numbers are either positive or negative.
Integer’s example: 12345
Fractions example: 0.1234
BCD: Binary Coded Decimal System
ASCII: American standard Code for Information Interchange
EBCDIC: Extended Binary Coded Decimal Interchange Code

Floating point: A number, which has both an integer part and a fractional part, is called a
real or a floating point number. These numbers can be either positive or negative.
The numbers are representing in scientific form.

Difference between fixed and floating point

Fixed Point: Decimal point has to be place by the user himself to the correct result. It
does not make any distinction between positive / negative number.

Floating point: Automatically keeps track of the position of the binary or decimal point.
If the number us negative it indicates as the result has 1 at the extreme left of the word.

Convert Binary into decimal:

a) (10101010)2  (?) 10

1
 Sreedhar’s CCE

1x27+0x26+1x25+0x24+1x23+0x22+1x21+0x20

128+0+32+0+8+0+2+0  170

Ans (10101010)2  (170)10

b) (10110.101)2  (?) 10

1x24+0x23+1x22+1x21+0x20+1x2-1+1x2-2+1x2-3

16+0+4+2+1/2+0/2+1/8

22+0.50+0.125 22.625

Ans (10110.101)2  (22.625) 10

c) (1011010)2  (?) 10

 1x26+0x25+1x24+1x23+0x22+1x21+0x20

 64+0+16+8+0+2+0 90

Ans (1011010)2  (90)10

d) (101.011)2  (?) 10

 1x22+0x21+1x20+0x2-1+1x2-2+1x2-3

 4+0+2+0/2+1/4+1/8

 5+.25+.125  5.375

Ans (101.011)2  (5.375)10

Convert the following Binary into Decimal:

a. (1101.101)2 b. (0.1011)2 c. (1001110.01)2 d. (101101.01)2

e. (1100001)2 f. (101101.1101)2 g. (10101.10101)2

Convert Decimal into Binary:

a) (123)10  (?) 2


2 123
2 61 1
2 30 1
2 15 0
2 7 1
2 3 1
1 1

Ans (123)10  (1111011) 2

2
 Sreedhar’s CCE

b) (344.25)10  (?) 2

 2 344
2 172 0
2 86 0 .25 x 2
2 43 0 0 .50 x 2
2 21 1 1 .00
2 10 1
2 5 0
2 2 1
1 0

Ans (344.25)10  (101011000.01) 2

c) (423.25)10  (?) 2

 2 423
2 211 1 .25 x2
2 105 1 0 .50x2
2 52 1 1 .00
2 26 0
2 13 0
2 6 1  01
2 3 0
1 1

Ans (423.25)10  (110100111.01) 2

Convert the following decimal to binary: a. (27.625)10 b. (463.5625)10

c. (25.3125)10 d. (48.1875)10 e. (0.625)10

Convert Decimal into Octal

a) (786.5)10  (?) 8

 8 786 .5x8
8 98 2 .40
8 12 2
1 4
 4
Ans (786.5)10  (1422.4) 8

b) (1489)10  (?) 8

 8 1489
8 186 1
8 23 2
2 7

Ans (1489)10  (2721) 8

3
 Sreedhar’s CCE

c) (572)10  (?) 8

 8 572
8 71 4
8 8 7
1 0

Ans (572)10  (1074) 8

d) (2508)10  (?) 8

 8 2508
8 313 4
8 39 1
4 7

Ans (2508)10  (4714) 8

Center the following Decimal into Octal

a. (2562)10 b. (2508)10 c. (28.125)10 d. (2345.25)10 e. (238.5)10 f. (9876)10

Convert Octal into Decimal:

a) (4567)8  (?)10

 4x83+5x82+6x81+7x80

 4x512+5x64+6x8+7x1

 2048+320+48+7

 2423

Ans (4567)8  (2423)10

b) (0.34)8  (?)10

 0x80+3x8-1+4x8-2

 0+3/8+4/64

 0+0.375+0.0625

 0.4375

Ans (0.34)8  (0.4375) 10

c) (426.40)8  (?)10

 8 426 Reminder
8 53 2
8 6 5
0 6
 .40 x 8=5

Ans (426.40)8  (652.5)10

Convert the following Octal to Decimal

a) (283)8 b) (2352)8 c) (765)8 d) (65.34)8

Convert Hexa to Decimal

4
 Sreedhar’s CCE

a) (BABA) 16  (?)10

 11x163+10x162+11x161+10x160
 11x4096+10x256+11x16+10x1
 45056+2560+176+10
 47802

Ans (BABA) 16  (47802)10

b) (ABCD) 16  (?)10

 10x163+11x162+12x161+13x160

 10x4096+11x256+12x16+13x1

 40960+2816+192+13

 43981

Ans (ABCD) 16  (43981)10

Convert the following Hexa to Decimal

a) (A029)16 b) (121B) 16 c) (A028)16 d) (15AE) 16

Convert Binary to Octal

a) (1011.1011)2  (?)8

 To convert the given number from binary to octal we will combine the digit in
groups of three adding leading of trailing Zeros wherever required.

1011.1011  001 011 . 101 100

1 3 . 5 4

 13.54

Ans (1011.1011)2  (13.54)8

b) (10110111.1)2  (?)8

10110111.1  010 110 111 . 100

2 6 7 . 4

Ans (10110111.1)2  (267.4)8

Convert Octal to Binary

a) (56.35)8  (?)2

56.35  5 6 . 3 5
101 110 . 011 101

 101110.011101

Ans (56.35)8  (101110.011101)2

b) (256)8  (?)2

 2 5 6
010 101 110
5
 Sreedhar’s CCE

 010101110

Ans (256)8  (10101110)2

Convert Binary to Hexa

a) (1011.1011)2  (?)16

 To convert the given number from binary to octal we will combine the digit in
groups of four adding leading of trailing Zeros wherever required.

 1011 . 1011
11 11

 11.11

Ans (1011.1011)2  (11.11)16

b) (10110111.1)2  (?)16

10110111.1  1011 0111 . 1000

11 7 . 8

Ans (10110111.1)2  (117.8)16

Convert Hexa to Binary

a) (AD5)16  (?)2

 A D 5
1100 1101 0101

Ans (AD5)16  (110011010101)2

b) (A29B) 16  (?)2

A29B  A 2 9 B
1010 0010 1001 1011

Ans (A29B) 16  (1010001010011011)2

c) (EF92)16  (?)2

 E F 9 2
1110 1111 1001 0010

Ans (EF92)16  (1110111110010010) 2

Convert Hexa to Binary

a) (3B8.D6)16 b) (A2B.9C) 16 c) (A9F8)16

Convert octal to Hexa

a) (605)8  (?)16
6
 Sreedhar’s CCE

This conversion can be down in two methods.

1. Octal to Decimal and Decimal to Hexa.

2. Octal to binary and binary to Hexa.

First Method

Step 1: Octal to Decimal

 6x82+0x81+5x80

 384+5

 (389)10

Step 2: Decimal to Hexa

(389)10  (?)16

 16 389
16 24 5
1 8

Ans (605)8  (185)16

Second Method

Step 1: Octal to Binary

(605)8  (?)2

 6 0 5
 110 000 101

 (110000101)2

Step 2: Binary to Hexa

(110000101)2  (?)16

 0001 1000 0101

 1 8 5

Ans (605)8  (185)16

Convert the following Octal to Hexa:

a) (725)8 b) (7375.71)8 c) (56.57)8 d) 7523)8

Convert Hexa to Octal

a) (6B.3A) 16  (?)8

7
 Sreedhar’s CCE

Step 1: Convert Hexadecimal to Decimal number.

Step 2: Convert decimal number to octal number.

Step 1.  6x161+11x160+3x16-1+10x16-2

 6x16+11x1+3/16+10/256

 96+11+0.1875+0.0390625

 (107.2265625)10

Step 2:  8 107 .2265625x8

8 13 3 1 .8125000x8
1 5 6 .5000000x8
4 .0000000
Ans (6B.3A) 16  (153.164)8