Binary to Decimal Converter

Binary to Decimal Converter

What is Binary to Decimal Conversion?

Binary to decimal conversion is the process of converting a binary number (a number expressed in the base-2 numeral system) into a decimal number (a number expressed in the base-10 numeral system). The binary system uses only two digits, 0 and 1, while the decimal system uses ten digits, from 0 to 9. Understanding how to convert binary to decimal is essential for working with binary data and calculations.

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Binary Number System

Binary is a base-2 numeral system used in mathematics and computer science. It uses only two symbols, 0 and 1, to represent numbers. Each digit in a binary number represents a power of 2. For example, the binary number “1010” represents (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 8 + 0 + 2 + 0 = 10 in decimal.

In computing, binary is fundamental as computers use binary digits (bits) to process and store information. It forms the basis for digital communication, data representation, and computer programming.

Decimal Number System

Decimal is the base-10 numeral system, the most commonly used system in everyday life. It uses ten symbols (0 to 9) to represent numbers. Each digit in a decimal number represents a power of 10. For example, the decimal number “325” represents (3 * 10^2) + (2 * 10^1) + (5 * 10^0) = 300 + 20 + 5 = 325.

How to Convert Binary to Decimal

Steps for Binary to Decimal Conversion:

1. Write down the binary number.
2. List the powers of 2 from right to left, starting with 20.
3. Multiply each binary digit by the corresponding power of 2.
4. Sum all the products.

Example:

Convert the binary number 11012 to decimal:

Write down the binary number: 11012

List the powers of 2 from right to left:

23, 22, 21, 20

Multiply each binary digit by the corresponding power of 2:

1 × 23 = 1 × 8 = 8

1 × 22 = 1 × 4 = 4

1 × 21 = 1 × 2 = 0

1 × 20 = 1 × 1 = 1

Sum all the products:

8 + 4 + 0 + 1 = 13

Therefore, the binary number 11012 is equal to the decimal number 1310

Binary to Decimal Conversion Table

Here is a table containing some binary to decimal converted numbers:

 Binary Number Decimal Number Hex Number 0 0 0 1 1 1 10 2 2 11 3 3 100 4 4 101 5 5 110 6 6 111 7 7 1000 8 8 1001 9 9 1010 10 A 1011 11 B 1100 12 C 1101 13 D 1110 14 E 1111 15 F 10000 16 10 10001 17 11 10010 18 12 10011 19 13 10100 20 14 10101 21 15 10110 22 16 10111 23 17 11000 24 18 11001 25 19 11010 26 1A 11011 27 1B 11100 28 1C 11101 29 1D 11110 30 1E 11111 31 1F 100000 32 20 1000000 64 40 10000000 128 80 100000000 256 100

Binary to Decimal Formula

Here is the Binary to Decimal formula:

FAQs on Binary to Decimal Converter

How to convert binary to decimal?

Converting binary to decimal involves multiplying each binary digit by its corresponding power of 2 and then adding up the results. Start from the rightmost digit and move to the left, with the rightmost digit corresponding to 2^0 (1) and each subsequent digit doubling in value (2^1, 2^2, 2^3, and so on).

How do you convert 10101 binary to decimal?

To convert 10101 binary to decimal: 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 16 + 0 + 4 + 0 + 1 = 21 (decimal)

How do you turn 1011 into a decimal?

To convert 1011 binary to decimal: 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 0 + 2 + 1 = 11 (decimal)

How to convert binary to decimal 111010?

To convert 111010 binary to decimal: 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 32 + 16 + 8 + 0 + 2 + 0 = 58 (decimal)

What is 1111 in decimal?

To convert 1111 binary to decimal: 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 4 + 2 + 1 = 15 (decimal)

How to convert 1100 binary to decimal?

To convert 1100 binary to decimal: 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 0 * 2^0 = 8 + 4 + 0 + 0 = 12 (decimal)

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