(PDF) Number System Notes Tutorial in English :- Infinity4Education
Computer Number Systems
What are the number systems in Computer?
Number systems are the
technique to represent numbers in the computer system architecture, every value
that you are saving or getting into/from computer memory has a defined number
system.
Computer architecture supports following number
systems.
- Binary
number system
- Octal
number system
- Decimal
number system
- Hexadecimal
(hex) number system
1) Binary Number System
A Binary number system has only two digits that
are 0 and 1. Every number (value) represents with 0 and 1 in this
number system. The base of binary number system is 2, because it has only two
digits.
2) Octal number
system
Octal number system has only eight (8) digits from 0
to 7. Every number (value) represents with 0,1,2,3,4,5,6 and 7 in this
number system. The base of octal number system is 8, because it has only 8
digits.
3) Decimal number
system
Decimal number system has only ten (10) digits from 0
to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this
number system. The base of decimal number system is 10, because it has only 10
digits.
4) Hexadecimal
number system
A Hexadecimal number system has sixteen (16)
alphanumeric values from 0 to 9 and A to F. Every
number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this
number system. The base of hexadecimal number system is 16, because it has 16
alphanumeric values. Here A is 10, B is 11, C
is 12, D is 13, E is 14 and F is 15.
Table of the Numbers Systems with Base,
Used Digits, Representation, C language representation:
Number
system
|
Base
|
Used
digits
|
Example
|
C
Language assignment
|
Binary
|
2
|
0,1
|
(11110000)2
|
int
val=0b11110000;
|
Octal
|
8
|
0,1,2,3,4,5,6,7
|
(360)8
|
int val=0360;
|
Decimal
|
10
|
0,1,2,3,4,5,6,7,8,9
|
(240)10
|
int
val=240;
|
Hexadecimal
|
16
|
0,1,2,3,4,5,6,7,8,9,
A,B,C,D,E,F |
(F0)16
|
int
val=0xF0;
|
Number System
Conversions
There are three types of conversion:
- Decimal
Number System to Other Base
[for example: Decimal Number System to Binary Number System] - Other
Base to Decimal Number System
[for example: Binary Number System to Decimal Number System] - Other
Base to Other Base
[for example: Binary Number System to Hexadecimal Number System]
Decimal Number
System to Other Base
To convert Number system from Decimal
Number System to Any Other Base is quite easy; you
have to follow just two steps:
A) Divide the Number (Decimal Number) by the base of target base system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16)).
B) Write the remainder from step 1 as a Least Signification Bit (LSB) to Step last as a Most Significant Bit (MSB).
A) Divide the Number (Decimal Number) by the base of target base system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16)).
B) Write the remainder from step 1 as a Least Signification Bit (LSB) to Step last as a Most Significant Bit (MSB).
Decimal
to Binary Conversion
|
Result
|
Decimal
Number is : (12345)10
|
Binary
Number is
(11000000111001)2 |
Decimal
to Octal Conversion
|
Result
|
Decimal
Number is : (12345)10
|
Octal
Number is
(30071)8 |
Decimal
to Hexadecimal Conversion
|
Result
|
Example
1
Decimal Number is : (12345)10 |
Hexadecimal
Number is
(3039)16 |
Example
2
Decimal Number is : (725)10 |
Hexadecimal
Number is
(2D5)16 Convert 10, 11, 12, 13, 14, 15 to its equivalent... A, B, C, D, E, F |
Other Base System
to Decimal Number Base
To convert Number System from Any Other
Base System to Decimal Number System, you have to follow
just three steps:
A) Determine the base value of source Number System (that you want to convert), and also determine the position of digits from LSB (first digit’s position – 0, second digit’s position – 1 and so on).
B) Multiply each digit with its corresponding multiplication of position value and Base of Source Number System’s Base.
C) Add the resulted value in step-B.
A) Determine the base value of source Number System (that you want to convert), and also determine the position of digits from LSB (first digit’s position – 0, second digit’s position – 1 and so on).
B) Multiply each digit with its corresponding multiplication of position value and Base of Source Number System’s Base.
C) Add the resulted value in step-B.
Explanation regarding examples:
Below given exams contains the following rows:
A) Row 1 contains the DIGITs of number (that is going to be converted).
B) Row 2 contains the POSITION of each digit in the number system.
C) Row 3 contains the multiplication: DIGIT* BASE^POSITION.
D) Row 4 contains the calculated result of step C.
E) And then add each value of step D, resulted value is the Decimal Number.
Below given exams contains the following rows:
A) Row 1 contains the DIGITs of number (that is going to be converted).
B) Row 2 contains the POSITION of each digit in the number system.
C) Row 3 contains the multiplication: DIGIT* BASE^POSITION.
D) Row 4 contains the calculated result of step C.
E) And then add each value of step D, resulted value is the Decimal Number.
Binary
to Decimal Conversion
|
Binary
Number is : (11000000111001)2
|
Octal
to Decimal Conversion
|
Result
|
Octal
Number is : (30071)8
|
=12288+0+0+56+1
=12345 Decimal Number is: (12345)10 |
Hexadecimal
to Decimal Conversion
|
Result
|
Hexadecimal
Number is : (2D5)16
|
=512+208+5
=725 Decimal Number is: (725)10 |
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