Decimal to Binary Converter
The Decimal to Binary Converter is a user-friendly online tool, to quickly convert between Decimal to Binary. with calculation table
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Decimal to Binary Converter
A Decimal to Binary Converter is a device that translates a number, from the decimal (base 10) system to the binary (base 2) system. For example, a binary representation is fundamental in computing, and this helps a lot. Converting decimal numbers to binary allows one to easily represent numbers in computers used to process.
Knowing Decimal and Binary Systems
Decimal System (Base-10): The ten-digit decimal system is used to represent numbers using 0 to 9. You know this system because it’s the one that most humans are already using.
Binary System (Base-2): In fact, a binary system uses only two digits – 0 and 1. Each position of a binary number represents a power of 2. It’s the language of computers, which use it to do calculations and store data.
How Many Decimal Digits in a Binary Number?
The number of decimal digits you can represent in binary varies because binary numbers don’t map directly to any particular number of decimal digits. In general, though:
Each binary digit, or bit, can take the value of either 0 or 1.
The length of the binary number increases logarithmically with respect to its decimal representation. For example:
8 in decimal is 1000 in binary, (4 bits).
255 in decimal is 11111111 in binary (8 bits).
So, with each step of increase in the decimal value, the binary number increases in size depending upon the power of 2 it needs.
Differences Between Decimal and Binary
| Aspect | Decimal (Base-10) | Binary (Base-2) |
|---|---|---|
| Digits | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 | 0, 1 |
| Base | 10 | 2 |
| Usage | Commonly used by humans for daily tasks | Used by computers for processing and storage |
| Example | 345 (decimal) | 101011001 (binary for 345 in decimal) |
How to convert decimal to binary
Here, we understand how to convert decimal integers to binary. Here, we will divide the decimal by 2 repeatedly. Let us use the decimal number 37 as an example. And divide it by 2 repeatedly.
37 divided by 2 repeatedly
37 ÷ 2 = 18 with a remainder of 1
18 ÷ 2 = 9 with a remainder of 0
9 ÷ 2 = 4 with a remainder of 1
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
Here you read the remainder in reverse order –
The remainder in reverse order is 100101. So, the decimal number 37 is equivalent to the binary number 100101.
Example, let’s convert 19 to binary:
19 ÷ 2 = 9 remainder 1
9 ÷ 2 = 4 remainder 1
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Now, reading from the bottom up, the binary representation of 19 is 10011.
Here, you have to divide the decimal number by 2 repeatedly in this process and note down the remainder, till the quotient becomes 0. The remainder, when read in reverse order, gives you the binary representation.
Frequently Asked Questions (FAQ)
1. Why do we have to convert decimal to binary?
The binary system is the basis of computer data processing because a computer has a simple matter of two states (on or off). With data being in a structure computers can process it efficiently, it is converted to binary.
2. So, how can I know that my binary-to-decimal conversion is correct?
To check we can go in the other direction and convert the binary result into decimal. If the decimal result equals (matches) the original number, the binary conversion is correct.
3. The question we need to answer is, why does binary only use two digits, 0 and 1?
Binary means the physical ‘on’ or ‘off’ states that digital devices use to process data, 1 = ‘on’, 0 = ‘off’.
4. How can we convert large decimal numbers to binary quickly?
The easiest and fastest way to go from a Decimal to a Binary is using a Decimal to Binary Converter. They are available online and can deal with very large numbers well.
5. How long does it take to represent a decimal number in binary?
In other words, the number of bits required depends upon the magnitude of the decimal number. For example:
To represent decimal 255 you have 8 bits (binary 11111111).
To store the decimal value for 1023, we use 10 bits — equal to binary 1111111111.
A table for Decimal to Binary conversion
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 5 | 101 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 50 | 110010 |
| 63 | 111111 |
| 100 | 1100100 |
| 1000 | 1111101000 |
| 10000 | 10011100010000 |
