Binary to Decimal Converter
Convert binary numbers to decimal by inputting a binary value and pressing convert.
Information on Number Conversion
A number system is a method of expressing numbers in a consistent manner using digits and numbers. There are different number system like, Decimal, Binary, Octal, Hexadecimal. These different number systems are used in different contexts.
Decimal Number System
Decimal number system is the most commonly used number system. It is a base 10 number system. It uses 10 digits from 0 to 9. The position of each digit in a decimal number denotes the power of 10. The rightmost digit is the ones place, the next digit to the left is the tens place, the next digit to the left is the hundreds place, and so on.
An example of a decimal number is
123410 = 1×103 + 2×102 + 3×101 + 4×100
Binary Number System
Binary number system is a base 2 number system. It uses only two digits, 0 and 1. The position of each digit in a binary number denotes the power of 2. The rightmost digit is the ones place, the next digit to the left is the twos place, the next digit to the left is the fours place, and so on.
An example of a binary number is
10112 = 1×23 + 0×22 + 1×21 + 1×20
How to convert Binary to Decimal?
To convert a binary number to decimal, you can use the following steps:
Step 1: Write down the binary number.
Step 2: Write down the decimal equivalent of each binary digit.
Step 3: Multiply each decimal equivalent by 2 raised to the power of the position of the digit.
Step 4: Add the results from step 3 to get the decimal equivalent of the binary number.
Example 1: Convert 100110100102 to (?)10
Step 1: Write down the binary number: 100110100102
Step 2-3:
| Binary | Number × 2 ^ i | Output | |
|---|---|---|---|
| 1 | 1 × 210 | 1024 | |
| 0 | 0 × 29 | 0 | |
| 0 | 0 × 28 | 0 | |
| 1 | 1 × 27 | 128 | |
| 1 | 1 × 26 | 64 | |
| 0 | 0 × 25 | 0 | |
| 1 | 1 × 24 | 16 | |
| 0 | 0 × 23 | 0 | |
| 0 | 0 × 22 | 0 | |
| 1 | 1 × 21 | 2 | |
| 0 | 0 × 20 | 0 | |
| 1024 + 128 + 64 + 16 + 2 = 1234 | |||
| The decimal Representation of (10011010010)2 is (1234)10 | |||
Example 2: Convert 111100010010000002 to (?)10
Step 1: Write down the binary number: 111100010010000002
Step 2-3:
| Binary | Number × 2 ^ i | Output | |
|---|---|---|---|
| 1 | 1 × 216 | 65536 | |
| 1 | 1 × 215 | 32768 | |
| 1 | 1 × 214 | 16384 | |
| 1 | 1 × 213 | 8192 | |
| 0 | 0 × 212 | 0 | |
| 0 | 0 × 211 | 0 | |
| 0 | 0 × 210 | 0 | |
| 1 | 1 × 29 | 512 | |
| 0 | 0 × 28 | 0 | |
| 0 | 0 × 27 | 0 | |
| 1 | 1 × 26 | 64 | |
| 0 | 0 × 25 | 0 | |
| 0 | 0 × 24 | 0 | |
| 0 | 0 × 23 | 0 | |
| 0 | 0 × 22 | 0 | |
| 0 | 0 × 21 | 0 | |
| 0 | 0 × 20 | 0 | |
| 65536 + 32768 + 16384 + 8192 + 512 + 64 = 123456 | |||
| The decimal Representation of (11110001001000000)2 is (123456)10 | |||
Binary to Decimal Conversion Table
The following table shows the common binary numbers equivalent decimal numbers:
| 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 |
Binary to Decimal converter
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