How to convert binary to decimal

# How to convert binary to decimal

Table of Contents

## Conversion Formula

Converting a binary number to a decimal number involves interpreting the binary digits (0s and 1s) as powers of 2 and adding them up. Here’s the general formula to convert a binary number to decimal:

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Given a binary number: b[n]b[n-1]…b[2]b[1]b[0]

The decimal equivalent is: D = b[n] * 2n + b[n-1] * 2(n-1) + … + b[2] * 22 + b[1] * 21 + b[0] * 20

Where:

• n is the highest power of 2 present in the binary number.
• b[i] represents the i-th binary digit (0 or 1) from right to left.

### Solved Examples

Example 1- Find the decimal value of 1110012

 power of 2: binary number: 1 1 1 0 0 1 25 24 23 22 21 20

Ans. 1110012 = 1⋅25+1⋅24+1⋅23+0⋅22+0⋅21+1⋅20 = 5710

Example 2- Find the decimal value of 1000112

 power of 2: binary number: 1 0 0 0 1 1 25 24 23 22 21 20

Ans. 1000112 = 1⋅25+0⋅24+0⋅23+0⋅22+1⋅21+1⋅20 = 3510

Also Read: Binary to Decimal converter

### Binary to decimal conversion table

 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 1101 13 1110 14 1111 15 10000 16 10001 17 10010 18 10011 19 10100 20 10101 21 10110 22 10111 23 11000 24 11001 25 11010 26 11011 27 11100 28 11101 29 11110 30 11111 31 100000 32 1000000 64 10000000 128 100000000 256

## FAQs on binary to decimal

### How do you convert 10101 binary to decimal?

To convert binary to decimal, multiply each binary digit by 2 raised to its respective position from right to left, starting with 0. Add up the results to obtain the decimal equivalent. For 10101: 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 16 + 0 + 4 + 0 + 1 = 21. o, 10101 in binary is equal to 21 in decimal.

### How to convert 1011 binary to decimal?

Convert binary to decimal by multiplying each binary digit by 2 raised to its respective position from right to left. For 1011: 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 0 + 2 + 1 = 11. Therefore, 1011 in binary is equivalent to 11 in decimal.

### What is 1111 in decimal?

To convert binary 1111 to decimal: 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 4 + 2 + 1 = 15 Hence, 1111 in binary is equal to 15 in decimal.

### What number is 11111111 in binary?

To convert binary 11111111 to decimal: 1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. Therefore, 11111111 in binary is equivalent to 255 in decimal.

### How do you write 255 in binary?

To convert decimal 255 to binary, repeatedly divide the number by 2 and note down the remainders in reverse order. For 255: 255 ÷ 2 = 127 remainder 1 127 ÷ 2 = 63 remainder 1 63 ÷ 2 = 31 remainder 1 31 ÷ 2 = 15 remainder 1 15 ÷ 2 = 7 remainder 1 7 ÷ 2 = 3 remainder 1 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 The remainders in reverse order give you the binary representation: 11111111.

### How do you write 32 in binary?

To convert decimal 32 to binary, apply the division-by-2 method: 32 ÷ 2 = 16 remainder 0 16 ÷ 2 = 8 remainder 0 8 ÷ 2 = 4 remainder 0 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 The remainders in reverse order give you the binary representation: 100000.

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