Table of Contents
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.
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:
- Write down the binary number.
- List the powers of 2 from right to left, starting with 20.
- Multiply each binary digit by the corresponding power of 2.
- 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)
