Question

Your computer uses 4 bits to represent decimal numbers (0, 1, 2, 3 and so on) in binary. What is the SMALLEST number
for which an overflow error occur?
A 14
B. 15
C. 16
D. 17

Answer 1

Answer:C-16

Explanation:

Answer 2

Using the concepts of binary/decimal conversions, and computer representations, it is found that option c, that is, 16, is correct.

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• In an unsigned n-bit arithmetic in a computer, the smallest number that can be represented is 0.
• The greatest number that can be represented is: $2^{n} - 1$
• If it is tried to represent a number greater than $2^n - 1$, an overflow error occurs, meaning that there are not enough bits to represent the desired quantity.

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• 4 bits are used to represent decimal numbers, thus, $n = 4$.
• The greatest number than can be represented is $2^4 - 1 = 16 - 1 = 15$.
• The next decimal number after 15 is 16, which is the first one to cause overflow.
• Thus, option C is correct.

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