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Number System

Binary-Decimal Conversion
 

Example
Find the decimal equivalent of binary number 11111.
Solution
The equivalent decimal number is,
= 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20
= 16 + 8 + 4 + 2 + 1 = ( 31 )10


Decimal-to Binary Conversion

 

Example
Express the 25.5 decimal number in the binary form.
Solution
Integer Part:

Thus, (25)10 = (11001)2
875.png 
Read down to up

Fraction part
880.png 
i.e., 0.510 = 0.12

Therefore 25.510 = 11001.12


Decimal-Octal Conversion

This can be achieved by dividing the given decimal number repeatedly by 8, until a quotient of 0 is obtained.
 

Example
Convert conversion (444.499)10.
Solution
Division Generated Remainder
444 / 8
55/ 8 885.png4
6/8 890.png7
0/8 895.png6

On reading the remainders from bottom to top, the decimal (444)10900.png(674)8. Now, fractional conversion

Multiplication Generated Integer
0.499905.png8 = 3.992 3
0.992 910.png8 = 7.936 7
0.936 915.png8 = 7.488 7
0.488920.png8 = 3.904 3

The process gets terminated when significant digits are acquired. Thus, octal equivalent is (444.499)10 = (674.3773)8


Octal-Binary Conversion

It can be explained through the following example: To convert (377)8 into binary, replace each significant digit by its 3-bit binary equivalent.

(377)8 = 3 7 7 = 011 111 111

Thus, (377)8 = (011111111)2


Binary-Hexadecimal Conversion

e.g., (10100110111110)2 = (0010 1001 1011 1110)2 = (2 9 B E)16 × 1


Hexadecimal-Binary Conversion

It can be explained through an example. To convert (1D5)16 into binary, replace each significant digit by its 4-bit binary equivalent.

(1D5)16 = 1 D 5

= 0001 1101 0101

Thus, (1D5)16 = (000111010101)2





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