Binary Number System

The binary number system is a radix-2 number system with ‘0’ and ‘1’.
All larger binary numbers are represented in terms of ‘0’ and ‘1’. The procedure for writing higher order binary numbers after ‘1’ is similar to the decimal number system.

e.g. First 16 numbers in the binary number system are, be 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110 and 1111. The next number after 1111 is 10000. Starting from the binary point, the place values of different digits in a mixed binary number are,
For integer value: 2^0, 2^1, 2^2 , 2^3, 2^4 etc.
for Fractional value: 2^−1, 2^−2, 2^−3, 2^-4 etc.

Bit is an abbreviation of the term ‘binary digit’ and is the smallest unit of information. It is either ‘0’ or ‘1’. A byte is a string of eight bits. The byte is the basic unit of data operated upon as a single unit in computers.

The 1’s complement of a binary number is obtained by  complementing all its bits, i.e. by replacing 0s with 1s and 1s with 0s. For example, the 1’s complement of (00110101)2 is (11001010)2. The 2’s complement of a binary number is obtained by adding ‘1’ to its 1’s complement. The 2’s complement of (00110101)2 is (11001011)2.

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