A-Level CS - Data Representation Fundamentals

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Binary Prefixes (e.g., Kibi vs. Kilo)

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Binary prefixes are powers of 1024 (2^10), whereas decimal prefixes are powers of 1000 (10^3). For example, 1 Kibibyte (KiB) = 1024 bytes, while 1 Kilobyte (KB) = 1000 bytes. This distinction is crucial for accurately calculating storage capacities and data rates in computing contexts.

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BCD (Binary Coded Decimal)

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BCD is a method of encoding decimal numbers where each digit is represented by its own 4-bit binary sequence (nibble). For example, the decimal number 25 is represented as 0010 0101 in BCD. It is commonly used in digital systems where easy decimal display is required, though it is less storage-efficient than pure binary.

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Two's Complement Representation

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A method for representing signed integers in binary. To negate a number, invert all bits and add 1. The most significant bit (MSB) acts as the sign bit (0 for positive, 1 for negative). For example, in an 8-bit system, +5 is 00000101, while -5 is 11111011. This simplifies arithmetic logic in hardware.

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Floating Point Normalisation

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Normalisation adjusts the mantissa and exponent so that the mantissa starts with '0.1' (for positive binary fractions), maximizing precision before the significant bits are lost. For example, converting 0.00101 x 2^3 to 0.101 x 2^1 retains more significant figures within the fixed bit-width of the register.

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Unicode vs. ASCII

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ASCII is a 7-bit code (often stored in 8 bits) representing 128 English characters and control codes. Unicode is a universal standard (like UTF-8, UTF-16) that uses variable bit lengths to represent characters from virtually all world languages, superseding the limitations of ASCII for internationalization.