Information Representation

• Binary prefixes (kibi, mebi, gibi, tebi) are powers of 1024; decimal prefixes (kilo, mega, giga, tera) are powers of 1000.
• Convert between denary, binary, hexadecimal and BCD; represent negative integers in one’s and two’s complement.
• Add and subtract in binary using two’s complement, and recognise overflow.
• BCD is used where each denary digit must be kept separate (displays, money); hexadecimal is a compact way for people to read binary.
• Characters are stored as codes from a character set: ASCII (7-bit), extended ASCII (8-bit) and Unicode (up to 4 bytes).
• A bitmap is a grid of pixels; file size ≈ width × height × colour depth. A vector graphic is a drawing list of objects and their properties.
• Sound is sampled: file size = sampling rate × sampling resolution × channels × time.
• Compression is lossless (exactly reversible, for example run-length encoding) or lossy (permanently discards data the user will not notice).

Prefixes, bases and conversions

Memory and storage sizes use two families of prefix. Decimal prefixes go up in powers of 1000; binary prefixes go up in powers of 1024 (2¹⁰). A drive sold as 4 GB holds 4 × 10⁹ bytes, while the operating system may report sizes in GiB.

The number bases you need are denary (base 10), binary (base 2) and hexadecimal (base 16, digits 0–9 then A–F for 10–15). One hex digit stands for exactly four bits (a nibble), so convert binary to hex by splitting into groups of four from the right.

Binary Coded Decimal (BCD) stores each denary digit separately in its own 4-bit nibble. 181 in BCD is 0001 1000 0001; it is not the same bit pattern as 181 in binary. The nibbles 1010 to 1111 are never used in BCD.

One’s and two’s complement

In one’s complement a negative number is formed by inverting every bit of the positive number. In two’s complement you invert every bit and then add 1. In two’s complement the most significant bit has a negative place value: in 8 bits it is −128, so the range is −128 to +127.

Binary addition subtract

Overflow