Digital circuits reliably distinguish two logic levels, represented as 0 and 1. Patterns of bits can encode numbers, text, images and sound.
The on/off switch picture is a simple model; actual logic levels correspond to defined voltage ranges.
Two logic states
Units
A bit is one binary digit; a nibble is four bits and a byte is eight.
Using decimal prefixes: kB = 1,000 bytes, MB = 1,000,000 bytes, and each larger SI prefix is a factor of 1,000. Binary prefixes KiB, MiB and GiB instead use factors of 1,024.
Place values (8-bit)
128, 64, 32, 16, 8, 4, 2, 1.
Reading unsigned 1011
Converting binary to denary
Add the place values where there is a 1. 1011 = 8 + 2 + 1 = 11. 11001010 = 128 + 64 + 8 + 2 = 202.
Converting denary to binary
Subtract place values or divide by 2. 13 = 8 + 4 + 1 = 1101. Pad with zeros to 8 bits: 00001101.
Range
n bits can store 2n different values: 8 bits → 256 (0 to 255); 16 bits → 65,536.
Patterns and unsigned range
Uses
Understanding binary is needed for storage, networking and data representation.
幻灯片
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