## Binary to Decimal (Base 2 to Base 10) Converter

Welcome to the Binary to Decimal Converter, a powerful tool that effortlessly converts binary numbers into their decimal equivalents. Whether you’re a computer programmer, digital enthusiast, or simply curious about number systems, this converter will streamline your binary to decimal conversions, making complex calculations a breeze.

## What are base number systems?

Base number systems, also known as numeral systems or radix systems, are ways of representing numbers that employ a specified base or radix. The number of distinct numbers or symbols utilized to denote a value in that system is indicated by the base. For example, the decimal system (base 10) employs ten distinct digits (0-9), but the binary system (base 2) employs only two (0 and 1) digits.

## How do I understand the concept of different bases?

Understanding various bases is analogous to how we comprehend numbers in our daily lives. Each point in a number in the decimal system indicates a power of ten. In decimal, the number “354” signifies (3 * 102) + (5 * 101) + (4 * 100). Each place in the binary system represents a power of two, and the number “101” in binary signifies (1 * 22) + (0 * 21) + (1 * 20).

## Why would I need to convert numbers between different bases?

Conversions of number systems are necessary in many domains, including computer programming, networking, and mathematics. Binary is commonly used in programming for low-level operations, whereas hexadecimal is utilized to express memory addresses and byte values. Because various systems may require distinct formats, converting across bases is critical for data transmission and storage.

## What is binary to decimal conversion?

Binary to decimal conversion involves transforming a binary number (base 2) into its corresponding decimal representation (base 10). In the binary system, each digit can only be 0 or 1, while in the decimal system, each digit ranges from 0 to 9.

## How does binary to decimal conversion work?

To convert a binary integer to decimal, multiply each digit by 2 raised to the power of its position from the rightmost digit (beginning with 0). Then add the results to get the decimal value.

## An example of binary to decimal conversion

``````Binary number: 1     1     0     1
Position:      3     2     1     0

Decimal value = (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= (1 * 8) + (1 * 4) + (0 * 2) + (1 * 1)
= 8 + 4 + 0 + 1
= 13
``````