The binary number system is base- Positional number representation. Every digit (a “bit”) is either or , and each position weighs twice as much as the one to its right.
Binary is what digital hardware natively speaks because every storage element and every signal wire is engineered to be in one of two states: low voltage or high voltage. Two states, two digits — the mapping is direct, and circuits don’t have to distinguish ten different voltage levels to do arithmetic.
To read a binary number, sum the powers of at the positions where the bit is . The bit at position contributes .
Fractional positions just continue the pattern with negative exponents: position contributes , position contributes , and so on.
The leftmost bit is the most significant bit (MSB) — it has the highest place value. The rightmost is the least significant bit (LSB).
For converting between binary and decimal in either direction, see Base Conversion. For interpreting binary numbers as signed quantities, see Signed binary number.