Binary to Decimal Converter
A binary to decimal converter is a helpful tool for converting any binary number to its equivalent decimal number system.
Binary Number System
A binary number system is a base-2 numeral system in which only 0 & 1 numeric values are used to express a number. This number system is widely used to represent data in computers and electronic systems.
Decimal Number System
A decimal number system is a base-10 numeral system in which 0, 1, 2, 3, 4, 5, 6, 7, 8, & 9 numeric values are used to express a number. Each digit of the decimal numbers counts the power of ten.
How to convert binary to decimal?
Binary to decimal conversion can be done easily by using our binary to decimal converter. Alternatively, there are two methods for binary to decimal conversion.
- Place Value Notation Method
- Doubling Method
Place Value Notation Method
Place value notation is a standard way of writing numbers, which takes the product of each digit by its place value. Below are the conversion steps for binary to decimal.
- Multiply each digit of a binary number by “2” and count the power of two from right to left, starting from 0. Such as 25, 24, 23, 22, 21, and 20
- Find the sum of all the products of binary digits with the place value exponent.
- The resultant sum will be the equivalent decimal number of the given binary number.
Doubling Method
The doubling method is another way to convert any binary number to its equivalent decimal number. Below are a few steps for binary to decimal conversion:
- Multiply the MSB (most significant bit) by “2” and add the second leftmost bit to it.
- Multiply the result by “2” and add the third leftmost bit to it.
- Continue the process until you add the LSB (least significant bit) to the result.
- The final result will be the equivalent decimal number of the given binary number.
Binary to decimal table
| Binary to Decimal Table | |
| Binary | Decimal |
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
Examples of binary to decimal conversion
Below are a few examples of binary to decimal conversion.
Example 1: By Place Value Notation Method
Convert (1011011)2 to its equivalent decimal number.
Solution
Step 1: Multiply each digit of the given binary number by 2.
(1011011)2 = (1 x 2) + (0 x 2) + (1 x 2) + (1 x 2) + (0 x 2) + (1 x 2) + (1 x 2)
Step 2: Add the powers of 2 from right to left.
(1011011)2 = (1 x 26) + (0 x 25) + (1 x 24) + (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20)
Step 3: Solve the exponents and multiply them by their corresponding binary digits.
(1011011)2 = (1 x 64) + (0 x 32) + (1 x 16) + (1 x 8) + (0 x 4) + (1 x 2) + (1 x 1)
(1011011)2 = (64) + (0) + (16) + (8) + (0) + (2) + (1)
Step 3: Now add all the exponents.
(1011011)2 = 64 + 0 + 16 + 8 + 0 + 2 + 1
(1011011)2 = 9110
Example 2: By Doubling Method
Convert (1110001)2 to its equivalent decimal number.
Solution
Step 1: Multiply the MSB (most significant bit) by “2” and add the second leftmost bit.
(1110001)2 = (1 x 2) + 1 = 3
Step 2: Multiply the above result by “2” and add the third leftmost bit.
(1110001)2 = (3 x 2) + 1 = 7
Step 3: Multiply the above result by “2” and add the 4th leftmost bit to it.
(1110001)2 = (7 x 2) + 0 = 14
Step 4: Multiply the above result by “2” and add the 5th leftmost bit.
(1110001)2 = (14 x 2) + 0 = 28
Step 5: Multiply the above result by “2” and add the 6th leftmost bit.
(1110001)2 = (28 x 2) + 0 = 56
Step 6: Multiply the above result by “2” and add the 7th leftmost bit.
(1110001)2 = (56 x 2) + 1 = 11310
You can also use our decimal to binary converter if you want to convert a decimal number to a binary number.