Understand that computers use binary to represent data (numbers, text,…

The idea

Computers store and process everything as binary patterns of 0s and 1s, because each bit is a two-state signal that hardware can hold reliably. The same bit pattern can stand for different things depending on how it is interpreted: a number, a character of text, a sample of sound, a pixel colour in a graphic, or part of a program instruction. For example, the 8-bit pattern 01000001 can be the unsigned integer 65 or the character 'A', depending on context. The number of distinct patterns a group of n bits can form is 2ⁿ, so 4 bits give 2⁴ = 16 states, 8 bits give 2⁸ = 256 states, and 10 bits give 2¹⁰ = 1024 states. The maximum number of states is therefore found by raising 2 to the power of the bit length; the highest unsigned value is one less than that count.

What earns the marks

• Binary uses only two symbols, 0 and 1, and each bit is a two-state unit that hardware can represent reliably.
• The same binary pattern can represent different data types, such as numbers, text characters, sound samples, graphic pixels or program instructions, depending on how it is interpreted.
• The number of distinct states for a pattern of n bits is 2ⁿ; for example 4 bits give 2⁴ = 16 states and 8 bits give 2⁸ = 256 states.
• The maximum number of states is calculated by raising 2 to the power of the bit length, not by multiplying the bit length by 2.
• The highest unsigned value representable by n bits is 2ⁿ − 1, which is one less than the number of states.

Common mistakes and how to put them right

• Multiplying the number of bits by 2 instead of using powers of 2.

  Put it right: The correct method is 2ⁿ, so 5 bits give 2⁵ = 32 states, not 10.

• Confusing the number of states with the highest value.

  Put it right: For 8 bits there are 256 states but the highest unsigned value is 255.

• Assuming a binary pattern has only one fixed meaning.

  Put it right: The same pattern can represent a number, a character, a sound sample or a graphic depending on the interpretation applied.

Exam tips

• Write the formula 2ⁿ before substituting the bit length, then evaluate the power carefully, for example 2⁶ = 64.
• Check whether the question asks for the number of states or the highest value; subtract 1 only when the highest unsigned value is required.
• Link each data type named in the question to a concrete example, such as 8 bits for a text character or a sound sample, to show understanding rather than just calculating.