# How does this number system conversion algorithm work?

• 0131313131313
In summary, the conversation discusses the conversion of the number 50 into binary and its relation to Egyptian and Russian multiplication methods. The link provided explains the process of using Russian multiplication to convert numbers into binary form. It is mentioned that this method is closely related to the binary representation of the number.
0131313131313
50 | 0
25 | 1
12 | 0
6 | 0
3 | 1
1 | 1
0

how does it work?

(I know how to use the algorithm... my question is about how it can do the conversion)

Looks like Egyptian multiplication.

No, I think he simply means conversion of 50 into binary. 50 = 110010 = 32+16+2.

CRGreathouse said:
Looks like Egyptian multiplication.

Yes, if you look at the link I posted this is the same thing as what I call Russian multiplication.

sjb-2812 said:
Yes, if you look at the link I posted this is the same thing as what I call Russian multiplication.

And this method, in turn, is closely related to the binary representation of the number.

## 1. What is a number system conversion algorithm?

A number system conversion algorithm is a mathematical process that allows us to convert a number from one number system (such as decimal) to another (such as binary or hexadecimal).

## 2. How does the algorithm determine which number system to convert to?

The algorithm uses the input number and a designated base for the desired number system to determine the conversion. For example, if the input number is in decimal and the desired number system is binary, the algorithm will use the base 2 to convert the number.

## 3. What is the step-by-step process of a number system conversion algorithm?

The first step is to divide the input number by the designated base of the desired number system. The remainder of this division becomes the rightmost digit of the converted number. The quotient is then divided by the base again, and the remainder becomes the next digit of the converted number. This process is repeated until the quotient becomes 0. The converted number is then read from right to left, with each digit representing a power of the designated base.

## 4. Can this algorithm convert any number from one system to another?

Yes, this algorithm can convert any positive integer from one number system to another. However, some limitations may exist for converting fractional numbers or negative numbers.

## 5. How accurate is a number system conversion algorithm?

A number system conversion algorithm is completely accurate as long as the input number and the designated base are correctly entered. However, the number of digits displayed in the converted number may be limited due to the limitations of the system being used to perform the conversion.

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