How to convert Quinary to Binary
Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. In the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220.A binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" and "1". The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices.
Formula
Follow these steps to convert a quinary number into binary form:
The simplest way is to convert the quinary number into decimal, then the decimal into binary form.
- Write the powers of 5 (1, 5, 25, 125, 625, and so on) beside the quinary digits from bottom to top.
- Multiply each digit by it's power.
- Add up the answers. This is the decimal solution.
- Divide the decimal number by 2.
- Get the integer quotient for the next iteration (if the number will not divide equally by 2, then round down the result to the nearest whole number).
- Keep a note of the remainder, it should be between 0 and 1.
- Repeat the steps from step 4. until the quotient is equal to 0.
- Write out all the remainders, from bottom to top. This is the binary solution.
| Digit | Power | Multiplication |
|---|---|---|
| 3 | 125 | 375 |
| 0 | 25 | 0 |
| 1 | 5 | 5 |
| 2 | 1 | 2 |
| Division | Quotient | Remainder |
|---|---|---|
| 382 / 2 | 191 | 0 |
| 191 / 2 | 95 | 1 |
| 95 / 2 | 47 | 1 |
| 47 / 2 | 23 | 1 |
| 23 / 2 | 11 | 1 |
| 11 / 2 | 5 | 1 |
| 5 / 2 | 2 | 1 |
| 2 / 2 | 1 | 0 |
| 1 / 2 | 0 | 1 |