Worksheet for Binary to Decimal, Hexa and Octal number conversion

The binary numeral system is 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. Binary Conversion is used to convert binary value into octal, decimal, hexa numbers. Here the following are employed to convert binary to decimal, Hex, Octal value. This below worksheet help you to understand how to perform all these conversion using base-2 number system.

Binary to Decimal Conversion: Since binary is a base-2 system, each digit represents an increasing power of 2, with the rightmost digit representing 2^{0}, the next representing 2^{1}, then 2^{2}, 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.

Example: 1010 is a binary value and here we converted into decimal
[(1) x 2^{3}] + [(0) x 2^{2}] + [(1) x 2^{1}] + [(0) x 2^{0}] = [1 x 8] + [0 x 4] + [1 x 2] + [0 x 1] = 10

Fractional decimal number 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 Hex 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:
1010010_{2} = 0101 0010 grouped with padding = 52_{16} 11011101_{2} = 1101 1101 grouped = DD_{16}

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.