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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
517.png 
Read down to up
Fraction part
522.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
 

 
On reading the remainders from bottom to top, the decimal (444)10542.png(674)8. Now, fractional conversion

Multiplication Generated Integer

 
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.

 



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.
 





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