A1.2.2 - How Data is Stored in Binary

Data Units

Integers are stored as fixed-width binary numbers — every value uses the same number of bits regardless of its size, ensuring consistent memory use.

Unsigned integers: Use all bits for magnitude. Maximum value = 2ⁿ−1 where n = number of bits. Only represent non-negative values. Example: 4-bit max = 1111 = 15.
Two's complement (signed integers): The most significant bit (MSB) is the sign bit — 0 = positive, 1 = negative. A 4-bit two's complement can represent −8 to +7. To get a negative number: flip all bits of the positive value, then add 1.

ASCII: 7-bit code. Represents 128 unique characters.
English letters, digits, punctuation. Example: 'A' = 1000001.
Unicode / UTF-8: Represents characters from all writing systems worldwide, not just English.
- Variable-width: uses 1 to 4 bytes per character depending on the character.
- Backward compatible with ASCII becpoupe the first 128 characters are identical.
- 'A' = 01000001 in UTF-8 (same as ASCII).
- Japanese, Arabic, emoji and other non-Latin characters require more than 1 byte.

Analogue sound waves must be converted to digital binary form through two steps:

Sampling: Measuring the amplitude (volume) of the wave at regular intervals. The number of measurements per second = sampling rate, measured in Hz. Higher rate = more detail = more data.
Quantization: Mapping each sample to the nearest value in a fixed set. The number of possible values = bit depth.
Each sample is then encoded as a binary number. Stereo audio stores two channels (left + right), doubling data size.

Video is a sequence of still images (frames) played at a rate that creates the illusion of motion.
Audio and video data are multiplexed (interleaved) to keep them synchronised during playback.
Video formats such as H.264 (AVC) and H.265 (HEVC) compress and encode the binary data for efficient storage and transmission.