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Number Systems: Question 9

Syllabus 1.1

Multiple choice 1 mark

A network engineer writes a printer's MAC address using hexadecimal digits, for example 3A-F1-9C-02-BB-E7, rather than writing out the full binary pattern.

What is the main reason hexadecimal is used for this purpose rather than binary?

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

Step 1: What hexadecimal actually represents

Hexadecimal is base 16, and each hexadecimal digit (0-9, then A-F for 10-15) can represent exactly 4 bits, since 4 bits can hold 16 different patterns (0000 to 1111). This means any binary pattern can be split into groups of 4 bits (nibbles) and each group rewritten as a single hexadecimal digit.

For example, one byte of the MAC address above, 3A, converts to binary as:

  • 3 = 0011
  • A = 10 in denary = 1010

Combining the nibbles: 3A = 00111010 in binary. Writing 3A is much shorter and easier for a person to read, type or compare than 00111010, but both represent exactly the same stored value (58 in denary).

Step 2: Why this matters for something like a MAC address

A full 48-bit MAC address would need 48 binary digits to write out in full, which is easy to mistype or misread. Written in hexadecimal, the same address needs only 12 hexadecimal digits (as in 3A-F1-9C-02-BB-E7), because each hexadecimal digit stands in for 4 binary digits. This compactness is purely for the convenience of the people reading, entering or comparing the address, the computer itself still stores and processes the value in binary either way.

Why the other options are wrong

  • A: incorrect, a computer’s memory stores every value in binary regardless of which base a person chooses to display it in; writing a value in hexadecimal does not shrink how it is physically stored.
  • C: incorrect, computers process everything using binary logic circuits internally; they do not require hexadecimal input, and no such conversion is forced before an address can be used.
  • D: incorrect. Hexadecimal is base 16, not a form of denary (base 10), and it is not automatically produced by the computer converting denary values.

Final answer

B, each hexadecimal digit stands for exactly 4 bits, making a long binary pattern far more compact and readable for people, without changing the value stored inside the computer.