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Data Representation and Multimedia: Question 6

Syllabus 1.1, 1.2, 1.3

Multiple choice AS 1 mark

A technician is converting numbers between denary (base 10) and hexadecimal by hand, using repeated division by 16 rather than converting through binary first.

Convert the denary number 91 into hexadecimal, using repeated division by 16 to find each hexadecimal digit.

What is 91 in hexadecimal?

Choose an answer to check it, then compare with the worked solution below.
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Worked solution

Dividing repeatedly by 16

To convert a denary number to hexadecimal using the division-remainder method, repeatedly divide by 16, recording the remainder at each step. The remainders form the hexadecimal digits, read from last to first.

Step 1: Divide 91 by 16.

91 / 16 = 5 remainder 11

(Check: 16 x 5 = 80, and 91 - 80 = 11, so the quotient is 5 and the remainder is 11.)

The remainder 11 is the least significant hexadecimal digit. Since hexadecimal digits above 9 are written as letters (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15), the remainder 11 is written as B.

Step 2: Divide the quotient (5) by 16.

5 / 16 = 0 remainder 5

The remainder is 5, written as the digit 5. Since the quotient is now 0, the division process stops.

Combining the digits

Reading the remainders from last calculated to first calculated gives the most significant digit first, then the least significant digit: 5, then B.

So 91 in hexadecimal is 5B.

Checking the answer

Convert 5B back to denary: 5 x 16 + 11 = 80 + 11 = 91, which matches the original number, confirming the conversion is correct.

Final answer

  • 5B (option A)