Question

A computer program uses 3 bits to represent integers. When the program adds the decimal (base 10) numbers 5 and 3, the result is 0. Which of the following is the best explanation for the result?1. An overflow error occured2. A round off error occured3. The result was affected by lost data compression4. The result was approximated by a floating point representation

Answer 1

Answer:

The correct option is 1 as the overflow error has occurred

Explanation:

As the program uses 3 bits to represent integers thus the range of the maximum value that the program can store is given as

$2^2+2^1+2^0=4+2+1=7$

So when the two numbers in decimal base 10 are added as 3 and 5 the resultant is given as

$3=(011)_2\\5=(101)_2\\\_\_\_\_\_\_\_\_\_\_\_\_\\8=(1000)_2$

This is more than what the 3 bit integer can store thus the overflow error has occurred.