Decimal to Binary
Different techniques can be used to convert from decimal to binary. Recursively dividing a given decimal value by two is one way to convert it from decimal to binary. The remainders are then recorded until the final quotient is equal to 0. These leftovers are then written in reverse order to produce the provided decimal number's binary equivalent. The mathematical representation of numbers using a set of digits or symbols is known as a number system. The decimal number system, the binary number system, the octal number system, and the hexadecimal number system are only a few examples of the various number systems. These are recognized with the aid of the base they possess. Using established conventions, converting numbers between different bases is simple.
Decimal to Binary Conversion
The total amount of digits employed in the number system determines the base, which is a property shared by all number systems. For instance, the binary number system, which only employs two digits to express numbers, has a base of 2. Similarly, the base of the decimal number system, which uses 10 digits to represent numbers, is 10. Before we convert numbers from decimal to binary, let's first learn the decimal and binary number systems.
Definition of the Decimal Number System
The decimal number system employs 10 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers having a base of 10. The Hindu-Arabic number system is another name for it. Each digit has a location that is ten times more important than before. For the representation of decimal fractions also employs a decimal point. For instance, if we use 36 as an example, 3 is 10 times greater than 6. The symbols for decimal numerals are 4510, 11810, and so forth. The numbers in this most well-known number system can be easily recognized even without the base being written down. In other words, a number is regarded as decimal if the basis is not specified.
How to convert decimal to binary?
Actions to convert:
- Divide the number by 2.
- Find the following iteration's integer quotient.
- Get the binary digit's remaining part.
- Till the quotient equals 0, keep going through the procedures.
Decimal to binary conversion table
| Decimal Number |
Binary Number |
Hex Number |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 10 | 2 |
| 3 | 11 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| 10 | 1010 | A |
| 11 | 1011 | B |
| 12 | 1100 | C |
| 13 | 1101 | D |
| 14 | 1110 | E |
| 15 | 1111 | F |
| 16 | 10000 | 10 |
| 17 | 10001 | 11 |
| 18 | 10010 | 12 |
| 19 | 10011 | 13 |
| 20 | 10100 | 14 |
| 21 | 10101 | 15 |
| 22 | 10110 | 16 |
| 23 | 10111 | 17 |
| 24 | 11000 | 18 |
| 25 | 11001 | 19 |
| 26 | 11010 | 1A |
| 27 | 11011 | 1B |
| 28 | 11100 | 1C |
| 29 | 11101 | 1D |
| 30 | 11110 | 1E |
| 31 | 11111 | 1F |
| 32 | 100000 | 20 |
| 64 | 1000000 | 40 |
| 128 | 10000000 | 80 |
| 256 | 100000000 | 100 |
