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Binary Formula

The Binary system is the number system that contains only 0s and 1s. Hence sometime its called as bits. The weight of each binary bit rely on its relative position within the number.The binary formula to convert decimal to binary is given by
Decimal to BinaryThe weight of the nth bit of the number starts from left hand side and decreases as it proceeds further to the right.

To convert binary to decimal the following chart is used and binary is noted as per the given decimal number
Binary to Decimal

Converting binary to decimal or decimal to binary is a easy task. But lot more things like one's complement, 2's complement, addition, subtraction, multiplication, divisionĀ are there in binary. Let see some few logic used to get them.

Addition has basic rules in binary:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 (CARRY 1)
1 + 1 + 1 = 11 (CARRY 1)

Subtraction has its own logic :
0 - 0 = 0
0 - 1 = (Take carry 1 from left)
1 - 0 = 1
1 - 1 = 0

Multiplication is bit different where the list of shifted multiplicands are added to get the multiplier digits as we do in normal multiplication. In division divide the dividend with divisor for the binary bits as you do in normal division.

Related Calculators
Binary Calculator Binary Conversion Calculator
Binary to Hex Calculator Convert Decimal to Binary Calculator
 

Binary Examples

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Lets see some examples on Binary examples:

Solved Examples

Question 1: Add the following: (11100)2 and (10110)2.
Solution:
 
Given digits are (11100)2 and (10110)2
    11
    11100
 + 10110
-----------
 110010
-----------
 

Question 2: Subtract (10001)2 from (11101)2
Solution:
 
 Given digits are 11101 and 10001
  11101
-10001
----------
 01100
----------


 

More topics in Binary Formula
Binary to Decimal Formula Decimal to Binary Formula
*AP and SAT are registered trademarks of the College Board.