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:
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
| binary number: | 1 | 1 | 1 | 0 | 0 | 1 |
| power of 2: | 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
| binary number: | 1 | 0 | 0 | 0 | 1 | 1 |
| power of 2: | 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.
