Decimal and binary are two different numeral systems used to represent numbers.
Decimal is the most common numeral system used by humans. It is a base-10 system, meaning it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit’s position in a decimal number represents a power of 10.
Binary is a base-2 numeral system, used primarily in digital electronics and computer systems. It uses only two digits: 0 and 1. Each digit’s position in a binary number represents a power of 2.
To convert a decimal number to binary, you can use a simple division method. Here’s a step-by-step process to convert a decimal number to binary:
| 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 |
To convert a decimal number to binary, use the division method. Divide the decimal number successively by 2, noting the remainders at each step. The binary representation is obtained by reading the remainders in reverse order.
The decimal number 10 can be converted to binary as follows: 10 ÷ 2 = 5 (Quotient), remainder 0 5 ÷ 2 = 2 (Quotient), remainder 1 2 ÷ 2 = 1 (Quotient), remainder 0 1 ÷ 2 = 0 (Quotient), remainder 1
The rules to convert decimal to binary are as follows: Divide the decimal number successively by 2. Write down the remainders at each step. Read the remainders in reverse order to obtain the binary representation.
The decimal to binary formula involves dividing the decimal number (N) by 2 repeatedly and noting the remainders (R) at each step. The binary representation is obtained by reading the remainders from bottom to top.
To represent 173 in 9-bit binary, first convert 173 to binary using the division method: 173 ÷ 2 = 86 (Quotient), remainder 1 86 ÷ 2 = 43 (Quotient), remainder 0 43 ÷ 2 = 21 (Quotient), remainder 1 21 ÷ 2 = 10 (Quotient), remainder 1 10 ÷ 2 = 5 (Quotient), remainder 0 5 ÷ 2 = 2 (Quotient), remainder 1 2 ÷ 2 = 1 (Quotient), remainder 0 1 ÷ 2 = 0 (Quotient), remainder 1
To convert 98.46 to binary, consider the integer and fractional parts separately. For the integer part (98), the binary representation is 1100010. For the fractional part (0.46), multiply it by 2 repeatedly, noting the integer part each time: 0.46 * 2 = 0.92 → 0 0.92 * 2 = 1.84 → 1 0.84 * 2 = 1.68 → 1 The complete binary representation of 98.46 is 1100010.0111011001 (rounded to the desired precision).
To convert 43 to binary: 43 ÷ 2 = 21 (Quotient), remainder 1 21 ÷ 2 = 10 (Quotient), remainder 1 10 ÷ 2 = 5 (Quotient), remainder 0 5 ÷ 2 = 2 (Quotient), remainder 1 2 ÷ 2 = 1 (Quotient), remainder 0 1 ÷ 2 = 0 (Quotient), remainder 1