Represent positive integers in binary

1.4.1 Data Types

Data Types — Note 2 of 10

Candidates should understand how and why computers store data as binary using switches, and that a binary number can have a variety of different interpretations depending on what is being stored (e.g. numeric, text, image, sound). Candidates should be able to convert positive whole numbers to binary and from binary to decimal/denary

What you need to know

Computers store all data in binary because their components (transistors) have two states. A binary number can represent a number, a character, part of an image or a sound sample: its meaning depends on how it is interpreted.

What to know

Computers use binary because their switches (transistors) have two states, on and off, which are reliable to distinguish.
The same bit pattern can represent different things (a number, text, part of an image or sound) depending on how it is interpreted.
Place values in 8 bits: 128 64 32 16 8 4 2 1.
Binary to denary: add the place values where there is a 1.
Denary to binary: working from the largest place value, put a 1 if it fits and subtract it, otherwise put 0.
With n bits, unsigned integers from 0 to 2^n - 1 can be represented.

Key terms

Binary: A base 2 number system using only the digits 0 and 1.

Exam technique

Tip:Write out the place value headings each time to avoid mistakes.

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