Computer Fundamentals

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Number Systems Number systems are the techniques to represent
numbers in the computer system architecture,
every value that we are saving or getting into/from
computer memory has a defined number system.
Types of Number Systems
1. Non-Positional Number Systems. Ex- I, II, II, IV…… etc.
2. Positional Number Systems.
a) Binary
b) Decimal
c) Octal
d) Hexadecimal
Base and Symbols of
Positional Number Systems
Number Systems Base Symbols
Binary 2 0, 1
Decimal 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Octal 8 0, 1, 2, 3, 4, 5, 6, 7
Hexa-
decimal
16
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D,
E, F

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4-bit Numbers with their
Decimal Values
Binary Decimal Equivalent
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
4- bit Numbers with their
Decimal Values (cont.)
Binary Decimal Equivalent
1000 8
1001 9
1010 10
1011 11
1100 12
1101 13
1110 14
1111 15
Bit is the smallest unit of data in computing. It is
represented by a 0 or a 1.
The byte is a unit of digital information that most
commonly consists of eight bits, representing a
binary number.

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In any binary number, the right most digit is
called least significant bit (LSB) and leftmost digit
is called most significant bit (MSB).
1 0 1 1 0
(MSB) (LSB)
Conversion Among Bases
• The possibilities:
Hexadecimal
Decimal Octal
Binary
Binary to Decimal Conversion
Technique
Multiply each bit by 2n, where n is the “weight”
of the bit
The weight is the position of the bit, starting
from 0 on the right
Add the results
Example
1010112 => 1 x 25 = 32
0 x 24 = 0
1 x 23 = 8
0 x 22 = 0
1 x 21 = 2
1 x 20 = 1
4310
Bit “0”

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Octal to Decimal Conversion
Technique
Multiply each bit by 8n, where n is the “weight”
of the bit
The weight is the position of the bit, starting
from 0 on the right
Add the results
Example
7248 => 7 x 82 = 448
2 x 81 = 16
4 x 80 = 4
46810
Hexadecimal to Decimal
Conversion
Technique
Multiply each bit by 16n, where n is the
“weight” of the bit
The weight is the position of the bit, starting
from 0 on the right
Add the results
Example
ABC16 => A x 162 = 10 x 256 = 2560
B x 161 = 11 x 16 = 176
C x 160 = 12 x 1 = 12
274810

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Decimal to Binary Conversion
Technique
Divide by two, keep track of the remainder
First remainder is bit 0 (LSB, least-significant
bit)
Second remainder is bit 1
Example
12510 = ?2
2 125
62 12
31 02
15 12
7 12
3 12
1 12
0 1
12510 = 11111012
Reverse Order
Octal to Binary Conversion
Technique
Convert each octal digit to a 3-bit equivalent
binary representation
Example
7058 = ?2
7 0 5
111 000 101
7058 = 1110001012

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Hexadecimal to Binary
Conversion
Technique
Convert each hexadecimal digit to a 4-bit
equivalent binary representation
Example
10AF16 = ?2
1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112