The relationship between the number of bits per character in a character…

The idea

A character set maps each character to a unique binary code. If a set uses n bits per character, each character is one n-bit pattern, so the number of distinct patterns is 2ⁿ. With 7 bits, 2⁷ = 128 characters can be represented, which covers standard ASCII. With 8 bits, 2⁸ = 256 characters, covering extended ASCII. Unicode uses more bits per character, so it can represent far more characters, including symbols and scripts from many languages. To work out capacity, identify the bits per character, then evaluate 2ⁿ. To work out bits needed for a required number of characters, find the smallest n where 2ⁿ is at least that number.

For example: 300 characters need 9 bits because 2⁸ = 256 is too few and 2⁹ = 512 is enough.

What earns the marks

• States that a character set assigns a unique binary code to each character.
• Uses the relationship that n bits per character give 2ⁿ possible characters.
• Correctly evaluates powers of two, such as 2⁷ = 128 and 2⁸ = 256.
• Explains that more bits per character increase the number of representable characters.
• Distinguishes ASCII, typically 7 or 8 bits per character, from Unicode, which uses more bits and supports many more characters.
• Applies the relationship to find the minimum bits needed for a given number of characters.

Common mistakes and how to put them right

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

  Put it right by treating each bit as doubling the number of patterns.

• Confusing bits per character with total bits in a message.

  Put it right by separating the code length for one character from the total for a string.

• Assuming Unicode uses a fixed small number of bits like ASCII.

  Put it right by noting Unicode uses more bits per character and therefore supports many more characters.

Exam tips

• Show the power-of-two calculation, for example 2⁷ = 128, rather than only stating the final number.
• When asked for the minimum bits, test powers of two in order until the required number of characters is reached.
• Use the terms bits per character and characters representable precisely, and link them with the 2ⁿ relationship.