Computer Architecture : Binary Arithmetic

Binary Addition :

Binary Addition is very similar to decimal addition, where the digits are added up and if carry results then that carry is forwarded to next digit for addition. Binary addition is no different from the decimal addition. The basic binary operations are shown below :

The first three additions are self explanatory, only the last one needs some explanation, in normal addition 1+1 is 2 but in binary number system decimal 2 is represented by 10. So the 0 is written in the given column and a carry of 1 over to the next column.

Example 1 : Lets see the addition of 110111 and 100101

The sum after adding 110111 and 100101 is 1011100.

Example 2 : Add Binary numbers 1011.101 and 0101.111

The sum after adding 1011.101 and 0101.111 is 10011.100

At the above example, the carry which is transferred from fractional part to integer part is called auxiliary carry.

Binary Subtraction :

Binary subtraction is done in similar manner as the decimal subtraction. the four basic cases of binary subtraction are as follows :

In the second case bigger number (1), is subtracted from the smaller one (0)2 for this borrow has to be taken from the next higher bit, this makes it (10)2, now (10)2 - (1)2 = (1)2 (ie, 2 - 1 = 1 in decimal). The following examples will help us to understand the subtraction.

Example 1 : Subtract 011 from 101

Thus binary difference is 010

Example 2 : Subtract 10011 from 11101

Thus the binary difference is 1010.

Binary Multiplication :

Multiplication in binary is similar to decimal multiplication. It is simpler than decimal multiplication because only 0s and 1s are involved. The Four basic cases of binary multiplication are :

Example 1 : Multiply (110)2 and (101)2

Thus (110)2 x (101)2 = (11110)2

Example 2 : Multiply (10110)2 and (1110)2

Thus (10110)2 x (1110)2 = (100110100)2

Binary Division :

The binary difference is not different to the decimal division. It is called as the long division procedure. The binary division is illustrated through the examples :

Example : Divide (1010)2 by (10)2

        Divider: (10)2 Dividend: (1010)2

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