Binary numeral system

The binary numeral system is a positional numeral system with base two, representing numbers using the digits 0 and 1. Each position represents a power of two.

Positional notation: A numeral system in which a digit’s value depends on its position and the system’s base. Binary assigns each position a successive power of two.
Digital electronics: Electronic circuits that process signals as discrete states, commonly represented by low and high voltages. Two-valued circuit states provide a physical counterpart to binary digits.
Pingala: An ancient Indian scholar whose work on poetic meters includes combinatorial methods associated with binary patterns. His treatment of syllable patterns is an early documented connection to binary enumeration.
Decimal numeral system: A positional numeral system with base ten, using the digits 0 through 9. Its familiar ten-symbol place values contrast with binary’s two-symbol powers of two.
Powers of two: Numbers formed by repeatedly multiplying two by itself, including 1, 2, 4, and 8. These are the place values that give binary digits their numerical weight.
Boolean algebra: An algebra of truth values with operations such as conjunction, disjunction, and negation. Its two-valued logic maps naturally to binary states in computing.
Gottfried Wilhelm Leibniz: A German polymath who developed and promoted systematic arithmetic in base two in the seventeenth century. He gave binary arithmetic a clear mathematical exposition and symbolic interpretation.
Hexadecimal numeral system: A positional numeral system with base sixteen, using digits 0 through 9 and letters A through F. Each hexadecimal digit compactly represents a group of four binary digits.
Binary addition: Addition of binary numerals using the digits 0 and 1 and carrying when a column totals two. Its carry rule follows directly from base two.
Bit: A binary digit, 0 or 1, and the basic unit of information in digital systems. Each binary numeral is a sequence of bits.

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