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Using this programming language a programmer attempts to add them in decimal values 14 and 15 and assing the sum to the variable “total”

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.

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Discussion:

Given that 4 bits are being used to represent the decimal values, the maximum decimal value that can be represented is 15 (1111 in binary).

The values 14 and 15 are both within the range of what can be represented by 4 bits individually.

Adding 14 (1110 in binary) and 15 (1111 in binary) together would result in 29 (11101 in binary), which exceeds what can be represented with 4 bits.

Therefore, the correct answer is:

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

Here’s a breakdown of why this is the most likely outcome:

  • Limited Representation: The 4-bit binary system can only represent values from 0 (0000) to 15 (1111).
  • Conversion to Binary: 14 in binary is 1110 and 15 in binary is 1111.
  • Addition Overflow: Adding these binary values (1110 + 1111) would result in a number larger than 1111 (which represents 15).

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Since the language is restricted to 4 bits, it cannot handle this sum (29) because it exceeds the maximum representable value (15).

This limitation triggers an overflow error, indicating that the operation cannot be completed correctly due to exceeding the system’s capacity.

Here’s why the other options are incorrect:

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

B. Incorrect: Both 14 and 15 can be represented individually in 4-bit binary. The issue arises during the addition.

D. Incorrect: Round-off error wouldn’t occur here because 14 and 15 have exact binary representations. The problem lies in the limited capacity for the sum.

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