Binary Converter

Binary Conversions


Binary Converter is an online tool specially programmed to perform the computations of Binary to Decimal Conversion, Binary to Hexadecimal Conversion and Binary to Octal Conversion

The binary numeral system is also called as base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Due to its basic implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers. Digital electronics only understand two states, ON and OFF. This is why digital electronics use the base-two, or binary, number system. In order design digital electronics, you will need to be proficient at calculate numbers from binary to decimal, Hexadecimal, octal etc.

Binary to Decimal Conversion

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 by:
[(1) x 25] + [(0) x 24] + [(0) x 23] + [(1) x 22] + [(0) x 21] + [(1) x 20] =
[1 x 32] + [0 x 16] + [0 x 8] + [1 x 4] + [0 x 2] + [1 x 1] = 37

Fraction Number Binary to Decimal Conversion

For example, the fractional binary number 010101 is converted to decimal form by
0 x 2-1 + 1 x 2-2 + 0 x 2-3 + 1 x 2-4 = 0.312

Binary to Hexadecimal Conversion

To convert a binary number into its hexadecimal equivalent, divide it into groups of four bits. If the number of bits isn't a multiple of four, simply insert extra 0 bits at the left are called padding. For example:
10100102 = 0101 0010 grouped with padding = 5216
110111012 = 1101 1101 grouped = DD16

Binary to Octal Conversion

Binary is also easily converted to the octal numeral system, since octal uses a radix of 8, which is a power of two. Converting from octal to binary proceeds in the same fashion as it does for hexadecimal: For example; 658 = 110 1012 178 = 001 1112

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