Binary Number System
Base-2 representation using only 0 and 1, the native language of digital hardware.
Definition
The binary number system represents numbers in base 2, using only the digits 0 and 1. Each position is a power of two, so the binary 1011 equals 8 + 0 + 2 + 1, which is 11 in decimal.
Fixed-point representation offers an alternative to floating point for fractions, placing an implied binary point at a fixed position. It trades dynamic range for predictable precision and speed, which suits signal processing and embedded systems where floating-point hardware is costly.
Beyond integers, binary underlies text encodings such as ASCII and Unicode, color values, and machine instructions, so a single bit pattern's meaning depends entirely on how software interprets it. This is why the same file can be read as text, an image, or code. Fluency in binary and hexadecimal, and awareness of word size and endianness, is what lets an engineer reason correctly about data at the level the hardware actually sees it.
Why base 2
- Two states map directly to a switch being off or on.
- Noise margins are wide with only two levels.
- Boolean logic operates naturally on binary digits.
Related representations
Hexadecimal (base 16) is a compact shorthand for binary, each hex digit standing for four bits. Signed integers use two's complement, and fractional values use floating point.
Why it matters
Binary is how all digital data, numbers, text, images, and instructions, is ultimately stored and manipulated. Understanding it is prerequisite to understanding overflow, precision, and encoding.
Fusion connection
Every diagnostic reading and control command in a fusion facility is encoded in binary; understanding the encoding guards against precision and range errors in acquired data.