Binary to Decimal

Free Binary to Decimal converter online. An online conversion tool for base 2 to base 10 conversions with fractional parts. Binary to decimal conversion calculator with detailed steps. An easy method of converting decimal to binary number equivalents is to write down the decimal number and continually divide-by-2 (two) to give a result. 

In the world of computing, binary, and decimal numbers play a fundamental role. Binary, the language of computers, consists of only two digits: 0 and 1. On the other hand, decimal is the numerical system most commonly used by humans, with a base of 10 and digits ranging from 0 to 9. Understanding how to convert binary to decimal and vice versa is essential for anyone seeking to delve into the inner workings of computers. In this blog, we will explore the process of converting binary numbers to their decimal equivalents, unraveling the mystery behind this seemingly complex task.


Binary Number System:

Before diving into the conversion process, let's quickly recap the binary number system. In binary, each digit represents a power of 2, starting from the rightmost digit. The rightmost digit holds the value of 2^0, the next one to the left holds 2^1, then 2^2, and so on. To express a value in binary, we combine the powers of 2 based on the digits present, using 1 to indicate the presence of that power and 0 to indicate its absence. For instance, the binary number 1010 represents 2^3 + 2^1 = 8 + 2 = 10 in decimal.


Binary to Decimal Conversion:

To convert a binary number to its decimal equivalent, we employ a straightforward method. We start from the rightmost digit (also known as the least significant bit) and move towards the left, multiplying each bit by the corresponding power of 2 and summing up the results. Let's illustrate this process with an example:

Example: Convert the binary number 1101 to decimal.

Step 1: Starting from the rightmost bit, we assign powers of 2 to each bit: 2^0, 2^1, 2^2, and 2^3. Binary Number: 1 1 0 1 Powers of 2: 2^3 2^2 2^1 2^0

Step 2: Multiply each bit by its corresponding power of 2: 1 * 2^3 = 8 1 * 2^2 = 4 0 * 2^1 = 0 1 * 2^0 = 1

Step 3: Sum up the results: 8 + 4 + 0 + 1 = 13

Therefore, the binary number 1101 is equivalent to the decimal number 13.


Shortcut Method:

For binary numbers with a large number of digits, calculating each power of 2 and multiplying it individually can be time-consuming. As a shortcut, we can start from the rightmost digit and double the previous result while adding the current bit. Let's use this shortcut to convert the binary number 1101 to decimal:

Starting from the rightmost bit: 1 (initial value) 1 * 2 + 0 = 2 2 * 2 + 1 = 5 5 * 2 + 1 = 11

The shortcut method yields the same result: 1101 (binary) = 13 (decimal).



Converting binary numbers to their decimal equivalents is a fundamental skill for anyone interested in computer science and programming. By understanding the principles of binary and decimal systems and following the conversion process described in this blog, you can bridge the gap between these two number systems. Mastering binary-to-decimal conversion allows you to decipher the language of computers, enabling you to work with binary data, perform calculations, and explore the intricate world of computer programming.