This document discusses different number systems used in computing including binary, decimal, octal, and hexadecimal. It explains that computers use binary to represent numbers internally and provides tables to demonstrate how to convert between the different bases. Examples are given of converting decimal numbers to their binary, octal, and hexadecimal equivalents through repeated division or grouping of bits. Readers are provided exercises to practice base conversion between the number systems.

1. Lecture no : 11
Introduction to Computer/ Computer
Education
Mr. Muhammad Moazzam
MPhil Public Health
BSc BioMedical
University of the Lahore

2. Numbering System
Base Conversion

3. Number systems
• Decimal – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Binary – 0, 1
• Octal – 0, 1, 2, 3, 4, 5, 6, 7
• Hexadecimal system – 0, 1, 2, 3, 4, 5, 6, 7, 8,
9, A, B, C, D, E, F
• ASCII

4. Why different number systems?
• Binary number result in quite a long string of
0s and 1s
• Easier for the computer to interpret input
from the user

5. Base Conversion
• In daily life, we use decimal (base 10) number
system
• Computer can only read in 0 and 1
– Number system being used inside a computer is
binary (base 2)
– Octal (base 8) and hexadecimal (base 16) are used
in programming for convenience

7. Quantities/Counting (1 of 2)
Decimal Binary Octal
Hexa-
decimal
0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 7 7

8. Quantities/Counting (2 of 2)
Decimal Binary Octal
Hexa-
decimal
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F

9. Conversion Among Bases
• The possibilities:
Hexadecimal
Decimal Octal
Binary

10. Binary and decimal system
• Binary to decimal
– X^27 + X^26+ X^25+X ^ 24 + X ^ 23+ X ^ 22+ X ^ 21 + X ^20
• Decimal to binary
– Keep dividing the number by two and keep track
of the remainders.
– Arrange the remainders (0 or 1) from the least
significant (right) to most significant (left) digits

11. Octal and Hexadecimal system
• Binary to Octal (8 = 23)
– Every 3 binary digit equivalent to one octal digit
• Binary to Hexadecimal (16 = 24)
– Every 4 binary digit equivalent to one hexadecimal digit
• Octal to binary
– Every one octal digit equivalent to 3 binary digit
• Hexadecimal to binary
– Every one hexadecimal digit equivalent to 4 binary digits

12. Base Conversion
• How to convert the decimal number to other
number system
– e.g. convert 1810 in binary form
2 |18 ----0
2 |09 ----1
2 |04 ----0
2 |02 ----0
1
– 1810 = 100102

13. Exercise
1-Convert 10001000(2) to Decimal.
2-Convert 1000111.001(2) to Decimal.
3-Convert 6767(10) to Binary.
4-Convert 186(10) to Hexadecimal.
5-Convert 5BD(16) to Decimal.
6-Convert 16AC(16) to Binary.
7-Convert 10001110(2) to Hexadecimal.
8-Convert 196(10) to Octal.

14. Exercise
9-Convert 0216(8) to decimal.
10-Convert 0216(8) to binary.
11-726(8) to decimal.
12-27FB16 to octal.
13-(104)10 to binary
14-(AF)16 to decimal.

15. Base Conversion
For example:
62 = 111110 = 76 = 3E
decimal binary octal hexadecimal
1 For Decimal:
62 = 6x101 + 2x100
2 For Binary:
111110 = 1x25 + 1x24 + 1x23 + 1x22 + 1x21 + 0x20
3 For Octal:
76 = 7x81+ 6x80
4 For Hexadecimal:
3E = 3x161 + 14x160
• Since for hexadecimal system, each digit contains number from 1 to
15, thus we use A, B, C, D, E and F to represent 10, 11, 12, 13, 14
and 15.