Data Representation covers how computers store different types of data using binary. Students learn number systems, character encoding, and how multimedia data is represented digitally.
Binary (base 2): each bit is 0 or 1. 8 bits = 1 byte. Range of n bits: 0 to 2ⁿ−1 (unsigned). Binary to denary: multiply each bit by its place value (128, 64, 32, 16, 8, 4, 2, 1). Hexadecimal (base 16): 0-9, A-F. Each hex digit = 4 binary bits. Used for: memory addresses, colour codes, MAC addresses (shorter than binary). Binary addition: carry when sum ≥ 2. Overflow: result exceeds available bits. Two\'s complement: represent negative numbers (flip bits + add 1). Signed byte range: -128 to +127.
Character encoding: ASCII (7 bits, 128 characters) and Unicode (up to 4 bytes, supports all languages). Each character has a unique code. Images: made of pixels. Each pixel has a colour code. Resolution (pixels) × colour depth (bits per pixel) = file size. Higher resolution/depth → larger file, better quality. Sound: sampled at regular intervals. Sample rate (samples/second) and sample resolution (bits per sample). Higher values → better quality, larger file. File size = sample rate × resolution × duration.
Reduces file size for storage/transmission. Lossy: permanently removes data (some quality lost). Used for: JPEG images, MP3 audio, MP4 video. Effective when small quality loss is acceptable. Lossless: reduces size without losing any data — original can be perfectly reconstructed. Methods: Run-Length Encoding (RLE) — stores repeated values as count + value. Used for: text files, medical images, PNG. Choice depends on: acceptable quality loss, required file size, data type.
Computers use binary because their electronic circuits have two states: on (1) and off (0). Transistors — the building blocks of processors — act as switches that are either conducting or not. Binary is the simplest, most reliable way to represent these two states. Using more states (like denary\'s 10) would require circuits to distinguish between 10 different voltage levels, which would be error-prone and slower. Binary is inherently resistant to electrical noise — any voltage above a threshold is 1, below is 0.
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