Question

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 the decimal values 14 and 15 and assign the sum to the variable total. Which of the following best describes the result of this operation?

Answer 1

Answer:

C

Explanation:

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

Answer 2

The term "bit" means binary digit, and it is used to represent data in a computer system. 4 bits can hold the sum of 14 and 15 because 4-bit is not large enough to represent 29 (an overflow will occur)

The maximum size of data an n-bit computer can hold is $2^n$

So, a 4-bit computer can hold a maximum of:

$Max = 2^4$

$Max = 16$

i.e a maximum of 16 digits

In binary, the digits are 0000 to 1111 i.e. from 0 to 15

So, when 14 and 15 are added, the result is:

$14 + 15 = 29$

The result is 29.

29 in binary is 11101

11101 is out of the range of the 4-bit binary sequence

Hence, an overflow will occur because 4-bit is not large enough to hold the sum

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