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In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" (zero) and "1" (one).

The decimal (base ten) numeral system has ten digits (0–9), whereas the binary system has two digits (0 and 1).

Similarly, in digital electronics, a binary signal is a signal that may assume only two possible values, for example an electrical voltage.

In computer science, the numerical values used in binary notation are typically zero and one.

The term also relates to computer hardware devices that have only two discrete states, on/off or false/true.

Early digital computers operated on decimal numbers through the use of special purpose mechanical adding machines called calculators with plugboard electromechanical control panels.

However, these machines could not process negative numbers nor fractions due to their design; they were full-adder machines which worked exclusively with natural numbers.

Since these early computers built everything out of individual mechanical relays it became tedious and expensive to constantly rewire them as new needs arose so instead be wired to perform specific functions.

Eventually people realized that this same functionality could be built out of a much smaller amount of on/off switches.

which led to the development of logic gates such as AND AND NOT and OR which allowed for Boolean algebra and ultimately digital computers.

Converting from decimal to binary is simple using this tool. Enter a decimal value into the box below and click 'Convert'. The conversion will happen automatically.