Limitations of binary data representation (Edexcel GCSE Computer Science): Flashcards

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Limitations of binary data representation
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Formula for number of patterns with nn bits

2n2^n

Number of values 4 bits can represent

16 values (24=162^4 = 16)

Number of values 8 bits can represent

256 values (28=2562^8 = 256)

Range of unsigned integers with 8 bits

0 to 255

Range of signed integers (two's complement) with 8 bits

-128 to +127

Trade-off of including negative numbers in signed integers

Cuts positive range in half

Number of patterns in 7-bit ASCII

128 patterns (27=1282^7 = 128)

Why ASCII is limited

Not enough patterns for other languages like Japanese or Arabic

How Unicode overcomes ASCII limitations

Uses more bits per character, represents 140,000+ characters

What colour depth determines

Bits used for each pixel's colour information

Number of colours with 4-bit colour depth

16 different colours (24=162^4 = 16)

Trade-off in image representation

Better quality means larger file sizes

What bit depth determines in audio

Volume levels per sound sample

Volume levels with 16-bit audio

65,536 levels (216=65,5362^{16} = 65,536)

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