AS · Practice questions · Binary and decimal prefixes

Powers of two.

Six original Cambridge-style questions on binary magnitudes and prefixes, with worked solutions.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

1000 or 1024.

Decimal: kilo 10³, mega 10⁶, giga 10⁹, tera 10¹² (steps of 1000).
Binary: kibi 2¹⁰, mebi 2²⁰, gibi 2³⁰, tebi 2⁴⁰ (steps of 1024).
Switching ladders: convert to bytes first, then divide by the other unit.
Bits and bytes: 1 byte = 8 bits; B is bytes and b is bits.

Recall

[2 marks]

State the number of bytes in (a) one mebibyte and (b) one megabyte.

(a) 2²⁰ = 1 048 576 bytes. ✓
(b) 10⁶ = 1 000 000 bytes. ✓

Explain

[2 marks]

Explain the difference between a kilobyte and a kibibyte.

A kilobyte uses a decimal prefix: 10³ = 1000 bytes. ✓
A kibibyte uses a binary prefix: 2¹⁰ = 1024 bytes, so it is slightly larger. ✓

Calculate

[2 marks]

A computer has 16 GiB of RAM. Calculate the number of bytes. Show your working.

1 GiB = 2³⁰ = 1 073 741 824 bytes. ✓
16 × 1 073 741 824 = 17 179 869 184 bytes (= 2³⁴). ✓

Convert

[2 marks]

A file is 6 291 456 bytes. Give its size in (a) MiB and (b) MB, to two decimal places.

(a) 6 291 456 ÷ 1 048 576 = 6.00 MiB. ✓
(b) 6 291 456 ÷ 1 000 000 = 6.29 MB. ✓

Analysis

[3 marks]

A customer buys a hard disk labelled 1 TB. Their operating system reports the capacity as 931 GB. Explain why, and show the calculation.

The manufacturer uses decimal prefixes: 1 TB = 10¹² bytes. ✓
The operating system divides by 2³⁰ (a gibibyte) but labels the result GB. ✓
10¹² ÷ 1 073 741 824 = 931.3, so no storage is missing. ✓

Apply

[3 marks]

A video camera records at 25 MiB per minute onto a card with 32 GiB of free space. Calculate the number of whole minutes of video that can be recorded.

32 GiB = 32 × 1024 = 32 768 MiB. ✓
32 768 ÷ 25 = 1310.72. ✓
1310 whole minutes (about 21 hours 50 minutes). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.