Binary to Decimal Converter
A binary to decimal converter is a tool or algorithm used to convert binary numbers (base-2) to their decimal equivalents (base-10). Understanding how to convert between binary and decimal is essential in computer science, digital electronics, and various other fields where binary numbers are commonly used.
Process of Conversion:
Understanding Binary and Decimal Systems:
- Binary system: In binary, numbers are represented using only two digits, 0 and 1. Each digit in a binary number represents a
power of 2, starting from the rightmost digit with 2^0, then 2^1, 2^2, and so on.
- Decimal system: In decimal, numbers are represented using ten digits, 0 through 9. Each digit in a decimal number represents a power of 10, starting from the rightmost digit with 10^0, then 10^1, 10^2, and so forth.
Conversion Algorithm:
- To convert a binary number to decimal, multiply each digit of the binary number by 2 raised to the power of its position, then sum up the results.
Example: Let’s take the binary number 10101 as an example and convert it to decimal.
Binary: 1 0 1 0 1
Starting from the rightmost digit (least significant bit):
- 1 * 2^0 = 1
- 0 * 2^1 = 0
- 1 * 2^2 = 4
- 0 * 2^3 = 0
- 1 * 2^4 = 16
Summing up the results: 1 + 0 + 4 + 0 + 16 = 21
Hence, the decimal equivalent of the binary number 10101 is 21.
Generalized Conversion:
- For a binary number with n digits (d_n, d_{n-1}, …, d_1, d_0), the decimal equivalent is given by: Decimal = d_n * 2^n + d_{n-1} * 2^{n-1} + … + d_1 * 2^1 + d_0 * 2^0