Question

Write a report about the overflow in digital field including examples

( please only typing I can’t understand the handwriting)

Answer 1

In digital overflow occurs in a condition such that if the size of result exceeds the magnitude in which the datatype can be can be represented .

for example in case of Arithmetic operations the size of result is too large and it is not suited to accommodate in the datatype,at this condition overflow occurs.Also note that, Overflow cannot occur in Addition or subtraction if the operands have different sign.

Consider the binary overflow example,

We have a number 255=11111111

adding bit 1 with 11111111=11111111 + 1= 0000000 result

In this case while we adding bits at the end there is no another bit for adding ,this case represent overflow error.

when there is no enough to hold the result ,This indicate binary overflow.

Arithmetic overflow with example ,

When the result of an arithmetic operation requires n+1 bits,upon operating on n-bits number,an overflow occurs.

let us consider 1001+1000=10001 the result contain 5 bits ,the 4-bits range is from 1 to 15 but the result obtained number is  17 ,so overflow occurs.

In case of signed arithmetic the overflow causes the sign bit of answer to change.In this case the overflow occurs if the result does not lie in the range .

In signed arithmetic overflow occurs only when two positive numbers or two negative numbers are added.

consider the example of addition of two positive numbers

0110+0101=1011 since the msb of result is 1,it reflects negative result which is incorrect , which means overflow has changed the sign of number.

consider the addition of negative numbers

take the two's complement of 6=1010

two's complement of 5=1011

ie,-6+-5=1010+1011=10101 here the msb is 0

Because in two's complement the carry generated after the addition is discarded and the result obtained here is declared positive

since the result is  positive number,this means overflow occur.