About Binary Numerals and Base-2 Computing

The binary numeral system is a positional notation with a radix or base of $b = 2$. Rather than utilizing ten distinct digits like the decimal system, binary employs only two symbols: $0$ and $1$.

Because electronic hardware relies on simple voltage states—high and low, or open and closed switches—binary serves as the foundational language of virtually all modern digital computers, microprocessors, and data storage systems.

Binary Digits and Character Set

Each individual binary digit is known as a bit. Combinations of bits allow systems to represent arbitrary numerical values, characters, and instructions by scaling across ascending powers of two:

Positional Structure and Calculation Example ($b = 2$)

Moving from right to left, each position in a binary string represents an increasing power of two ($2^0, 2^1, 2^2, 2^3, \dots$).

To evaluate a multi-position binary value like 1011, the computation expands into standard polynomial form:

• Byte Grouping: Bits are typically grouped into sets of eight, known as bytes, which can represent $2^8 = 256$ distinct values.
• Boolean Algebra: Binary logic aligns directly with truth values in logic systems, allowing hardware circuits to execute complex arithmetic and decision-making tasks using logic gates.