# Binary to Decimal

## Binary to Decimal converter

Up to 63 binary characters can be converted to Decimal. Use the left field below to enter any binary value, such as 1010, and then click the Convert button to use the new binary decimal conversion tool. The outcome is displayed in the right field below.

## Binary System

The base of the binary numeral system is two (radix). It only has two numbers since it uses the base-2 numeral system: 0 and 1.

The binary system has been used for many reasons in ancient Egypt, China, and India. Still, in the modern era, it has taken on the role of the language of electronics and computers. This one is the most effective method for determining whether an electric signal is off (0) or on (1). It also serves as the foundation for the binary code computers utilize to construct data. Binary numerals are used in even the digital text you are reading right now.

Despite appearances, reading a binary number is simple: Every digit in a binary number is raised to the power of 2, starting with the rightmost digit (20) since this is a positional system. Each binary digit in the binary system denotes a single bit.

## Decimal System

The decimal numeral system is the most widely used and accepted system in daily life. It bases itself on the number 10. (radix). Consequently, it has ten symbols: The digits 0 through 9, namely 0, 1, 2, 3, 4, 5, 6, 7, and 9.

Many ancient civilizations used the decimal numeral system, which is one of the earliest numeral systems that is now known. The Hindu-Arabic numeral system solved the problem of representing huge numbers in the decimal system. The Hindu-Arabic numeral system assigns positions to the digits of a number. This system uses powers of base 10 to calculate numbers, and the digits are raised to the nth power according to their placements.

**Consider the decimal number 2345.67 as an example:**

The number 5 is in the place of ones (100 equals 1), and the number 4 is in the place of tens (101)

(102) 2 is in the position of thousands, and 3 is in the hundreds (103)

In the meantime, the digits 6 and 7 are in the tenths (1/10, which is 10-1) and the hundredths (1/100, which is 10-2) positions, respectively, after the decimal point.

Therefore, the following is another way to express the number 2345.67: (2 * 103) + (3 * 102) + (4 * 101) + (5 * 100) + (6 * 10-1) + (7 * 10-2)

## Understanding Binary Numbers

A basic understanding of interpreting a binary number may be helpful when converting binary to Decimal. Each bit (binary digit) in the binary positional system is a power of two, as was already mentioned. Every binary integer, with the rightmost one in the position of 20, might therefore be expressed as a power of two.

As an illustration, the binary value (1010)2 can also be expressed as (1 * 23) + (0 * 22) + (1 * 21) + (0 * 20).

## How to Convert Binary to Decimal

There are two ways to convert from binary to Decimal. The first one uses the binary's positional representation, as previously mentioned. The second technique, double dabbles, is used to convert lengthier binary sequences quickly. The jobs are not utilized.

**Steps to convert binary to Decimal**

**Step 1:** Write down the binary number.

**Step 2:** Multiply each digit by the positional value, beginning with the least significant number (LSB, which is the rightmost one. Keep doing this until the most crucial digit (MSB - the leftmost one).

**Step 3:** Add the outcomes to obtain the specified binary number's decimal equivalent.

## How to convert binary to decimal?

**For binary number with n digits:**

*d _{n-1} ... d_{3} d_{2} d_{1} d_{0}*

The decimal number is equal to the sum of binary digits (d_{n}) times their power of 2 (2^{n}):

decimal = *d*_{0}×2^{0} + *d*_{1}×2^{1} + *d*_{2}×2^{2} + ...

#### Example

Find the decimal value of 111001_{2}:

binary number: | 1 | 1 | 1 | 0 | 0 | 1 |
---|---|---|---|---|---|---|

power of 2: | 2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |

111001_{2} = 1⋅2^{5}+1⋅2^{4}+1⋅2^{3}+0⋅2^{2}+0⋅2^{1}+1⋅2^{0} = 57_{10}

## Binary to decimal conversion table

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 |