# A certain programming language uses 4-bit binary sequences to represent nonnegative integers

A certain programming language uses 4-bit binary sequences to represent nonnegative integers. For example, the binary sequence 0101 represents the corresponding decimal value 5.

Using this programming language a programmer attempts to add them in decimal values 14 and 15 and assing the sum to the variable “total”. Which of the following best describes the result of this operation?

A. The correct sum of 29 will be assigned to the variable “total”

B. an overflow error will occur because 4 bits is not large enough to represent either of the values 14 or 15

C. an overflow error will occur because 4 bits is not large enough to represent 29, the sum of 14 and 15.

D. a round-off error will occur because the decimal values 14 and 15 are represented as approximations due to the fixed number of bits used to represent numbers.

**Answer:**

C. an overflow error will occur because 4 bits is not large enough to represent 29, the sum of 14 and 15

**Reason:**

In this scenario, a programmer attempts to add 14 and 15 using a programming language that restricts numbers to 4-bit binary sequences.

While both 14 and 15 can be individually represented in this system (as 1110 and 1111 respectively), adding them creates a problem.

With only 4 bits, the language can only handle values from 0 to 15. Since the sum of 14 and 15 (29) exceeds this limit, an overflow error will occur.

The addition cannot be performed correctly because the result falls outside the range of numbers the system can represent.

Here’s why the other options are incorrect:

A. Incorrect: The sum (29) cannot be assigned to the variable as 4 bits can’t represent it.

B. Incorrect: Both 14 and 15 can be represented in 4-bit binary (1110 and 1111 respectively). The issue arises during the addition.

D. Incorrect: Round-off error wouldn’t occur here because the values 14 and 15 can be precisely represented in the system. The problem lies in the limited capacity for the sum.