## COMPUTER ARITHMETIC

Computer arithmetic is a field of computer science that investigates how computers should represent numbers and perform operations on them.

## BINARY ARITHMETIC

Binary arithmetic includes the basic arithmetic operations of addition,subtraction,multiplication and division.It has only two to digits:0and1.

### Binary addition

The addition table for binary arithmetic consists of only the following five entries:

- 0+0=0
- 0+1=1
- 1+0=1
- 1+1=0 (plus a carry of 1 to next higher column)
- 1+1+1=11(carry 1 to the next)

**Note:**1 is the largest digit in binary number system.

### Binary subtraction

If the subtrahend(the lower digit) is larger than the minuend(the upper digit),it is necessary to borrow from the column to the left.In decimal 10 is borrowed,in binary 2 is borrowed,in octal 8 is borrowed,and in hexadecimal 16 is borrowed.

The subtraction table for binary arithmetic consists of only the following four entries:

- 0-0=0
- 0-1=1(with a borrow from the next column)
- 1-0=1
- 1-1=0

Additive method of subtraction is known as complementary subtraction.

### Binary multiplication

The multiplication table for binary arithmetic consists of only the following four entries:

- 0×0=0
- 0×1=0
- 1×0=0
- 1×1=1

### Additive method of binary multiplication:-

Computers can perform multiplication operation by the way of addition also.Ex:We can obtain 4*8 by adding the digit 8 four times(8+8+8+8).### Binary Division

The division table for binary arithmetic consists of only the following four entries:

- 0÷0= Divide by zero error
- 0÷1=0
- 1÷0=Divide by zero error
- 1÷1=1

Division by zero in any number system is meaningless,computers deal with this problem by raising an error condition called 'Divide by zero' error.

### Additive method of binary division:-

Computers can perform even division operation by the process of addition also.A computer performs division operation by repeating complementary subtraction method.

Ex:- we can obtain 35÷5 as follows:

- 35-5=30
- 30-5=25
- 25-5=20
- 20-5=15
- 15-5=10
- 10-5=5
- 5-5=0

Divisor is subtracted repeatedly from the dividend until the result of subtraction becomes less than or equal to zero.