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:
- 4-bit binary representation: With 4 bits, you can represent values from 0 (0000) to 15 (1111).
- Adding 14 and 15: In decimal, 14 + 15 = 29.
- Overflow: Since 29 is greater than the maximum value representable by 4 bits (15), attempting this addition will cause an overflow error. The 4-bit binary system cannot hold the sum.
In simpler terms: Imagine a small box with four compartments to hold balls. If you try to put more than four balls (15) in the box, you’ll have extras that won’t fit (overflow).
Other options are incorrect because:
A. Incorrect: The sum (29) cannot be stored correctly, so it’s not assigned.
B. Incorrect: Both 14 and 15 can be represented within the 4-bit limit (0-15).
D. Incorrect: Round-off error applies to situations where numbers are represented with a limited number of decimal places, not binary bits.