Question

Write the short notes on computer arithmetic

Answer 1

Answer:

Computer arithmetic is a branch of computer engineering that deals with methods of representing integers and real values (e.g., fixed- and floating-point numbers) in digital systems and efficient algorithms for manipulating such numbers by means of hardware circuits or software routines.

Negative Number Representation

Sign Magnitude

Sign magnitude is a very simple representation of negative numbers. In sign magnitude the first bit is dedicated to represent the sign and hence it is called sign bit.

Sign bit ‘1’ represents negative sign.

Sign bit ‘0’ represents positive sign.

In sign magnitude representation of a n – bit number, the first bit will represent sign and rest n-1 bits represent magnitude of number.

 

For example,

+25 = 011001

Where 11001 = 25

And 0 for ‘+’

-25 = 111001

Where 11001 = 25

And 1 for ‘-‘.

Range of number represented by sign magnitude method = -(2n-1-1) to +(2n-1-1) (for n bit number)

But there is one problem in sign magnitude and that is we have two representations of 0

+0 = 000000

– 0 = 100000

 

2’s complement method

To represent a negative number in this form, first we need to take the 1’s complement of the number represented in simple positive binary form and then add 1 to it.

For example:

(-8)10 = (1000)2

1’s complement of 1000 = 0111

Adding 1 to it, 0111 + 1 = 1000

So, (-8)10 = (1000)2

Please don’t get confused with (8)10 =1000 and (-8)10=1000 as with 4 bits, we can’t represent a positive number more than 7. So, 1000 is representing -8 only.

Range of number represented by 2’s complement = (-2n-1 to 2n-1 – 1)

Explanation:

hope it helps u

:)