This document discusses different number systems used in computers. It defines decimal, binary, octal, and hexadecimal number systems and provides examples of each. The key steps to convert between these number systems are described, including dividing the number by the base of the target system and reading remainders from bottom to top. Class work questions are provided to have students define each number system and do example conversions between binary, octal, and hexadecimal.

2. TPTG 620
Presentation
Subject: Computer
Grade: 8th
Topic: Number System
Muhammad Jawad Aziz
BC190402944

3. Learning Objectives
WHAT IS NUMBER SYSTEM?
DIFFERENT TYPES OF NUMBER SYSTEM
LIKE DECIMAL, BINARY, OCTALAND HEXADECIMAL
NUMBER SYSTEM
 CONVERTING ONE NUMBER SYSTEM TO
OTHER NUMBER SYSTEM

4. Define Number System OR
What is number System?
NUMBER SYSTEM IS DEFINED AS “THE TECHNIQUE TO
REPRESENT AND WORK WITH NUMBERS IS
CALLED NUMBER SYSTEM”.
WE HAVE HEARD VARIOUS TYPES OF NUMBER
SYSTEMS SUCH AS THE WHOLE NUMBERS AND THE
NATURAL NUMBERS. BUT IN THE CONTEXT OF COMPUTERS,
THE TYPES OF NUMBER SYSTEMS ARE:
THE DECIMAL NUMBER SYSTEM
THE BINARY NUMBER SYSTEM
THE OCTAL NUMBER SYSTEM
THE HEXADECIMAL NUMBER SYSTEM

5. Types of Number Systems
THERE ARE THE FOUR MAIN TYPES OF NUMBER SYSTEMS.
DECIMAL NUMBER SYSTEM (BASE - 10)
BINARY NUMBER SYSTEM (BASE - 2)
OCTAL NUMBER SYSTEM (BASE - 8)
HEXADECIMAL NUMBER SYSTEM (BASE - 16)
WE WILL STUDY EACH OF THESE SYSTEMS ONE BY ONE IN DETAIL

6. What is decimal Number System?
DECIMAL NUMBER SYSTEM IS ALSO KNOWN AS BASE 10 SYSTEM.
THE DECIMAL NUMBER SYSTEM USES TEN DIGITS: 0,1,2,3,4,5,6,7,8 AND 9
THE DECIMAL NUMBER SYSTEM IS THE SYSTEM THAT WE GENERALLY
USE IN OUR REAL LIFE.
IF ANY NUMBER IS REPRESENTED WITHOUT A BASE, IT MEANS THAT
ITS BASE IS 10.
FOR EXAMPLE:
(12)10, (345)10, (119)10, (200)10, (3139)10 ARE SOME EXAMPLES OF
NUMBERS IN THE DECIMAL NUMBER SYSTEM

7. Number System?
BINARY NUMBER SYSTEM IS ALSO KNOWN AS BASE 2 SYSTEM.
THE BINARY NUMBER SYSTEM USES 2 DIGITS: 0 AND 1
DIGITS 0 AND 1 ARE CALLED BITS AND 8 BITS TOGETHER MAKE A BYTE.
THE DATA IN COMPUTERS IS STORED IN TERMS OF BITS AND BYTES.
FOR EXAMPLE:
(111)2, (1010)2, (101)2, (10001)2 ARE SOME EXAMPLES OF NUMBERS IN
THE BINARY NUMBER SYSTEM

8. System?
OCTAL NUMBER SYSTEM IS ALSO KNOWN AS BASE 8 SYSTEM.
THE OCTAL NUMBER SYSTEM USES 8 DIGITS: 0,1,2,3,4,5,6, AND 7
OCTAL NUMBER SYSTEM IS ALSO A POSITIONAL VALUE SYSTEM WITH
WHERE EACH DIGIT HAS ITS VALUE.
FOR EXAMPLE:
(67)8, (10450)8, (335)8, (1234567)8 ARE SOME EXAMPLES OF NUMBERS IN
THE BINARY NUMBER SYSTEM

9. What is Hexadecimal Number System?
BINARY NUMBER SYSTEM IS ALSO KNOWN AS BASE 16 SYSTEM.
THE HEXADECIMAL NUMBER SYSTEM USES SIXTEEN DIGITS/ALPHABETS:
0,1,2,3,4,5,6,7,8, 9 AND A,B,C,D, E, F . HERE A TO F OF THE HEXADECIMAL
SYSTEM MEANS THE NUMBERS 10 TO 15 RESPECTIVELY.
THIS SYSTEM IS USED IN COMPUTERS TO REDUCE THE LARGE-SIZED
STRINGS OF THE BINARY SYSTEM.
FOR EXAMPLE:
(A9)16, (9BCF)16, (D56)16, (1092C)16 ARE SOME EXAMPLES OF NUMBERS IN
THE BINARY NUMBER SYSTEM

10. Conversion Rules of Number Systems
A NUMBER CAN BE CONVERTED FROM ONE NUMBER SYSTEM
TO ANOTHER NUMBER SYSTEM. LIKE BINARY NUMBERS CAN
BE CONVERTED TO OCTAL NUMBERS AND VICE VERSA,
OCTAL NUMBERS CAN BE CONVERTED TO DECIMAL
NUMBERS AND VICE VERSA AND SO ON. LET US SEE THE
STEPS REQUIRED IN CONVERTING THESE NUMBER SYSTEMS.

11. Conversion of Binary / Octal / Hexadecimal
Number Systems to Decimal Number Systems
TO CONVERT A NUMBER FROM THE BINARY/OCTAL/HEXADECIMAL SYSTEM TO THE
DECIMAL SYSTEM, WE USE THE FOLLOWING STEPS.
BINARY TO DECIMAL
EXAMPLE: (100111)2
SOLUTION:
STEP # 1: IDENTIFY THE BASE OF THE GIVEN NUMBER. HERE, THE BASE IS 2.
STEP # 2: MULTIPLY EACH DIGIT OF THE GIVEN NUMBER, STARTING FROM THE
RIGHTMOST DIGIT, WITH THE BASE. (1 X 2) + (0 X 2) + (0 X 2) + (1 X 2) + (1 X 2) + (1
X 2)
STEP # 3: THE EXPONENTS SHOULD START WITH 0 AND INCREASE BY 1 EVERY TIME
AS WE MOVE FROM RIGHT TO LEFT. (1 X 25) + (0 X 24) + (0 X 23) + (1 X 22) + (1 X 21)
+ (1 X 20)
SINCE THE BASE HERE IS 2, WE MULTIPLY THE DIGITS OF THE GIVEN NUMBER.
(100111)2 = (1 X 25) + (0 X 24) + (0 X 23) + (1 X 22) + (1 X 21) + (1 X 20)
= (1 X 32) + (0 X 16) + (0 X 8) + (1 X 4) + (1 X 2) + (1 X 1)
= 32 + 0 + 0 + 4 + 2 + 1
= 39

12. Octal To Decimal
EXAMPLE: (10027)8
SOLUTION:
STEP # 1: IDENTIFY THE BASE OF THE GIVEN NUMBER. HERE,
THE BASE IS 8.
STEP # 2: MULTIPLY EACH DIGIT OF THE GIVEN NUMBER,
STARTING FROM THE RIGHTMOST DIGIT, WITH THE BASE. (1 X 8)
+ (0 X 8) + (0 X 8) + (2 X 8) + (7 X 8)
STEP # 3: THE EXPONENTS SHOULD START WITH 0 AND
INCREASE BY 1 EVERY TIME AS WE MOVE FROM RIGHT TO LEFT.
(1 X 84) + (0 X 83) + (0 X 82) + (2 X 81) + (7 X 80)
SINCE THE BASE HERE IS 8, WE MULTIPLY THE DIGITS OF THE
GIVEN NUMBER.
(10027)8 = (1 X 84) + (0 X 83) + (0 X 82) + (2 X 81) + (7 X 80)
= (1 X 4096 ) + (0 X 512) + (0 X 64) + (2 X 8) + (7 X 1)
= 4096 + 0 + 0 + 16 + 7
= 4119

13. Hexadecimal to Decimal
EXAMPLE: (1AF9)16
SOLUTION:
STEP # 1: IDENTIFY THE BASE OF THE GIVEN NUMBER. HERE, THE BASE IS
16.
STEP # 2: MULTIPLY EACH DIGIT OF THE GIVEN NUMBER, STARTING FROM
THE RIGHTMOST DIGIT, WITH THE BASE.
(1 X 16) + (A X 16) + (F X 16) + (9 X 16)
(1 X 16) + (10 X 16) + (15 X 16) + (9 X 16)
STEP # 3: THE EXPONENTS SHOULD START WITH 0 AND INCREASE BY
1 EVERY TIME AS WE MOVE FROM RIGHT TO LEFT.
(1 X 163) + (10 X 162) + (15 X 161) + (9 X 160)
SINCE THE BASE HERE IS 16, WE MULTIPLY THE DIGITS OF THE GIVEN
NUMBER.
(1AF9)16 = (1 X 16) + (A X 16) + (F X 16) + (9 X 16)
= (1 X 16) + (10 X 16) + (15 X 16) + (9 X 16)
= (1 X 163) + (10 X 162) + (15 X 161) + (9 X 160)
= (1 X 4096) + (10 X 256) + (15 X 16) + (9 X 1)
= 4096 + 2560 + 240 + 9
= 6905

14. Conversion of Decimal Number System to Binary /
Octal / Hexadecimal Number System
TO CONVERT A NUMBER FROM THE DECIMAL
NUMBER SYSTEM TO BINARY/OCTAL/HEXADECIMAL
NUMBER SYSTEM, WE USE THE FOLLOWING
STEPS. THE STEPS ARE SHOWN ON HOW TO CONVERT
A NUMBER FROM THE DECIMAL SYSTEM TO THE
OCTAL SYSTEM.
EXAMPLE:
CONVERT (4320)10 INTO THE OCTAL SYSTEM.
SOLUTION:
STEP 1: FIRSTLY WE CONVERT THE GIVEN NUMBER
INTO DECIMAL NUMBER SYSTEM IF THE NUMBER IS
INTO OTHER THAN DECIMAL NUMBER SYSTEM.
STEP 2: IDENTIFY THE BASE OF THE REQUIRED
NUMBER. SINCE WE HAVE TO CONVERT THE GIVEN
NUMBER INTO THE OCTAL SYSTEM, THE BASE OF
THE REQUIRED NUMBER IS 8.
STEP 3: DIVIDE THE GIVEN NUMBER BY THE BASE

15. 8 4320
8 540 0
8 67 4
8 8 3
8 1 0
Step 3: The given number in the octal number system is obtained just by
reading all the remainders and the last quotient from bottom to top
8 4320
8 540 0
8 67 4
8 8 3
8 1 0
(4320)10 = (10340)8

16. Class Work
DEFINE THE FOLLOWING TERMS
 BINARY NUMBER SYSTEM
 OCTAL NUMBER SYSTEM
 DECIMAL NUMBER SYSTEM
 HEXADECIMAL NUMBER SYSTEM
CONVERT (11100111)2 INTO OCTAL NUMBER SYSTEM
CONVERT (9ADC03)16 INTO BINARY NUMBER SYSTEM