How to convert Binary to Quinary
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.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.
Formula
Follow these steps to convert a binary number into quinary form:
The simplest way is to convert the binary number into decimal, then the decimal into quinary form.
- Write the powers of 2 (1, 2, 4, 8, 16, and so on) beside the binary 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 5.
- Get the integer quotient for the next iteration (if the number will not divide equally by 5, then round down the result to the nearest whole number).
- Keep a note of the remainder, it should be between 0 and 4.
- 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 quinary solution.
| Digit | Power | Multiplication |
|---|---|---|
| 1 | 32 | 32 |
| 0 | 16 | 0 |
| 0 | 8 | 0 |
| 1 | 4 | 4 |
| 0 | 2 | 0 |
| 1 | 1 | 1 |
| Division | Quotient | Remainder |
|---|---|---|
| 37 / 5 | 7 | 2 |
| 7 / 5 | 1 | 2 |
| 1 / 5 | 0 | 1 |