Number System Conversion

BINARY (2) OCTAL (8) DECIMAL (10) HEXADECIMA
L (16)
0000 0 0 0
0001 1 1 1
0010 2 2 2
0011 3 3 3
0100 4 4 4
0101 5 5 5
0110 6 6 6
0111 7 7 7
1000 8 8
1001 9 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
DIGITAL NUMBER SYSTEM CONVERSION


NUMBER SYSTEM
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
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.
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.
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.
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 14, E is 15 and F is 16.
Number system
Base(Radix)
Used digits
Example
Binary
2
0,1
(11110000)2
Octal
8
0,1,2,3,4,5,6,7
(360)8
Decimal
10
0,1,2,3,4,5,6,7,8,9
(240)10
Hexadecimal
16
0,1,2,3,4,5,6,7,8,9,
A,B,C,D,E,F
(F0)16
CONVERSIONSDECIMAL TO OTHER
1. DECIMAL TO BINARY
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).

, Decimal to Binary Conversion
Result
Decimal Number is : (12345)10
Binary Number is
(11000000111001)2
2. DECIMAL TO OCTAL
Decimal to Octal Conversion Result
Decimal Number is : (12345)10
Octal Number is
(30071)8
3. DECIMAL TO HEXADECIMAL
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
BINARY TO OTHER
A) Multiply the digit with 2(with place value exponent). Eventually add all the multiplication
becomes the Decimal number.
1. BINARY TO DECIMAL
2. BINARY TO OCTAL
An easy way to convert from binary to octal is to group binary digits into sets of three, starting
with the least significant (rightmost) digits.
Binary: 11100101 = 11 100 101
011 100 101 Pad the most significant digits with zeros if
necessary to complete a group of three.
Then, look up each group in a table:
Binary:
000 001 010 011 100 101 110 111Octal:
0
1
2
3
4
5
6
7
Binary = 011 100 101
Octal =