To Learn How to use Binary Number System, go to 'Lesson:Data Representation.

Binary number

Binary Number System is a Place value system.

In the binary system there are to sysmbols or possible digit values, 0 and 1. Even so, this base-2 system can be used to represent any quantity that can be represented in decimal or other number systems. It is a positional-value system, wherein each binary digit has its own value or weight expressed as power of 2 (Look at the picture on left).

Binary system lends the most convenient implementation in digital systems. It is very difficult to design an electronic equipment so that it can work with 10 different voltage levels(if we implement the Decimal Number System). It is very easy to design simple, accurate electronic circuits that operate with only two voltage levels. For this reason, almost every digital system uses the binary system as the basic number system of its operations.

Place values in binary ns

Positional values in binary numbers

The sequence of binary number goes as 00, 01,10,11,100,101,110,111,1000, ... so on. The binary counting sequence has an important characteristic. The units bit(LSB) changes either from 0 to 1 or 1 to 0 with each count. The second bit stays at 0 for two counts, then at 1 for two counts, then at 0 for other two counts, and so on. The third bit stays at 0 for four counts, then at 1 for four counts, and so on. The fourth bit stays at 0 for eight counts, then at 1 for eight counts and so on. If we wanted to count further we would add more places, and this pattern would continue with 0s and 1s alternating in groups of 2n - 1.