## Convert from Binary to Decimal

Convert from Binary to Decimal :Binary is the most basic type of number system, employing only two digits of 0 and 1. (i.e. value of base 2). Because digital electronics only have two states (either 0 or 1), binary numbers are most commonly used by computer engineers, networking and communication specialists, and other professions.

Binary to decimal conversion is the process of converting a number in the binary number system to its decimal counterpart. A number system is a format for representing numbers in a certain manner. The binary number system is used to represent data in computers and electrical devices and consists of only two numbers, 0 and 1.

The decimal number system is the most widely used and simply understood number system on the planet. There are two ways for converting binary to decimal: the positional notation approach and the doubling method. Let’s look at some binary to decimal conversion examples to discover how to convert binary to decimal.

## Binary System

The binary numeral system is based on the number 2. (radix). It is a base-2 numeral system with only two numbers: 0 and 1.

While it was used for many reasons in ancient Egypt, China, and India, the binary system has since become the language of electronics and computers in the modern world. This is the most efficient approach for detecting the off (0) and on (1) states of an electric signal. It also serves as the foundation for binary code, which is utilized to construct data in computer-based devices. Even the digital text you’re reading right now is made up of binary integers.

Because number numbers are a positional number system. That is, for the integer portion, the weight of the places from right to left is 2^{0}, 2^{1}, 2^{2}, 2^{3}… and so on, while for the fractional part, the weight is 2^{-1}, 2^{-2}, 2^{-3}, 2^{-4}… and so on.

Decimal | Binary |

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

## Decimal System

The decimal number system is the most widely used and accepted system in everyday life. Its foundation is the number ten (radix). As a result, it has ten symbols: The digits 0 through 9; specifically, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Many ancient civilizations utilized the decimal number system, which is one of the earliest known numerical systems. The Hindu-Arabic numeral system solved the problem of expressing very big numbers in the decimal system. The Hindu-Arabic numeral system assigns places to the digits in a number using powers of ten; digits are raised to the nth power in line with their location.

Binary | Decimal |

0 | 0 |

1 | 1 |

10 | 2 |

11 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

1000 | 8 |

1001 | 9 |

1010 | 10 |

1011 | 11 |

1100 | 12 |

### Steps for Converting Binary to Decimal

- Write the supplied binary number first, then count the powers of 2 from right to left (powers starting from 0)
- Now, from right to left, write each binary digit with the matching powers of 2 from right to left, so that the first binary digit (MSB) is multiplied by the biggest power of 2.
- In the preceding stage, combine all of the products.
- The final solution will be the decimal number necessary.

**1: Convert the binary number 1011 to a decimal number.**

Solution: Given, Binary number = 1011_{2}

Hence, using the binary to decimal conversion formula, we have:

1001_{2} = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)

= 8 + 0 + 2 + 1

(11)_{₁₀}

**2. Convert binary number 10.101 into decimal number. **

Solution: Given, Binary Number = 10.101_{2}

10.101_{2} = (1 × 2¹) + (0 × 2⁰) + (1 x 2^{-1})+( 0 x 2^{-2} ) + (1 x 2^{-3} )

10.101_{2} = 8+0+2+0+0.5+0+0.125

(10.625)_{₁₀}

### Making Use of Doubling for Convert from Binary to Decimal

This is a basic way for converting a binary number to a decimal number; you must begin with the leftmost digit (or MSB) from the input. Take the most significant bit (MSB), straight down, then multiply by 2 and add the second leftmost bit, store it as the current result, then multiply by 2 again and add the third leftmost bit, update this value as the current result, and repeat until the least significant bit is added (LSB or rightmost bit). This procedure is called as Doubling since you are doubling (multiplying by 2) each time.

These are basic algorithms that are detailed in stages below.

- Make a note of the binary number.
- Begin by doubling your previous sum and adding the current digit.
- Add the next leftmost digit to your existing total.
- Repeat the previous step.

**1. Convert binary number 1110 into decimal number **

= (1110)Related posts_{2}= 1 = 12+1 =3 = 32+1=7 = 72+0=14 = (14)_{10}