What is Binary?

Binary describes a numbering scheme in which there are only two possible values for each digit: 0 and 1. The term also refers to any digital encoding/decoding system in which there are exactly two possible states. In digital data memory, storage, processing, and communications, the 0 and 1 value are sometimes called "low" and "high," respectively.

Discrete elements of information are represented in a digital system by physical quantities called signals. Electrical signals such as voltages and currents are the most common. Electronic devices called Transistors predominate in the circuitry that implements these signals. The signals in most present‐day electronic digital systems use just two discrete values and are therefore said to be binary. A binary digit, called a bit, has two values: 0 and 1. Discrete elements of information are represented with groups of bits called binary codes. For example, the decimal digits 0 through 9 are represented in a digital system with a code of four bits (e.g., the number 7 is represented by 0111).

Since binary is a base-2 system, each digit represents an increasing power of 2, with the rightmost digit representing 20, the next representing 21, then 22, and so on. To determine the decimal representation of a binary number simply take the sum of the products of the binary digits and the powers of 2 which they represent. For example, the binary number 100101 is converted to decimal form as follows:

1001012 = [ ( 1 ) × 25 ] + [ ( 0 ) × 24 ] + [ ( 0 ) × 23 ] + [ ( 1 ) × 22 ] + [ ( 0 ) × 21 ] + [ ( 1 ) × 20 ]

1001012 = [ 1 × 32 ] + [ 0 × 16 ] + [ 0 × 8 ] + [ 1 × 4 ] + [ 0 × 2 ] + [ 1 × 1 ]

1001012 = 3710

Octal number

The conversion from binary to octal is easily accomplished by partitioning the binary number into groups of three digits each, starting from the binary point and proceeding to the left and to the right.

Hexadecimal

Conversion from binary to hexadecimal is similar, except that the binary number is divided into groups of four digits:

Let us see the tabular column comparison to decimal number to its binary number, octal, hexadecimal.