# Changing number bases directly

• elcotufa
In summary, the teacher is teaching students how to change a base number directly into another base number without changing to a different number system like base 10 or base 2. The steps are to recognize what the digits in the number represent in the new base, and to use that information to work out the number in the new base. There is no set formula, and it is up to the individual to be able to do this.
elcotufa

## Homework Statement

How do you change a base into another number directly without changing to base 10 or base 2 for example?

Eg

changing 1442 base 6 to base 3 = 112022

Just want to know the steps in the division

Teacher wants us to do it this way for less error

Help appreciated

elcotufa said:

## Homework Statement

How do you change a base into another number directly without changing to base 10 or base 2 for example?

Eg

changing 1442 base 6 to base 3 = 112022

Just want to know the steps in the division

Teacher wants us to do it this way for less error

Help appreciated

I don't think there there is a formula per se.

If you are not to convert to base 10 at all, then I think you need to recognize what the digits in base 6 represent in base 3.

Hence in the ones digits you have
1,2,3,4,5 base 6 convert to 1,2,10,11,12 base 3.
10,20, ... base 6 is 20,110,200,220,1010 base 3.
100, 200, ... base 6 is 1100,2200,11000,12100,20200 base 3
1000, 2000 ... base 6 is 22000,121000, ... etc. base 3

Then you can assemble in base 3 least significant first as below to get what the number represents. (But remember you must use base 3 addition to get your result.)

1442 = 2 + 220 + 12100 + 22000 = 222 + 101100 = 112022

Thanks, I am kinda getting the idea

The way I saw it done was dividing 1442 /3 for base 6 to base 3 but the numbers do not match probably

and for 112022 is by dividing by 20 (number 6 in base 3)

I'm missing the counting technique when dividing or just suck at itThis is basicly what he has
Code:
11
3  \ 1442
332    2
110    2
22    0
4     2
1     1
0     1

I can see that 22 times 3 is 66 but 110 in base 3, but I am wondering if there is an easy method, for example counting with the two ones in the top of fours

from base 3 to base 6 it was
Code:
202
20  |   112022
2101       2
101        11
1         11
0         1

Using leftovers down to top for the numberThere is no method other than knowing what each number is in different bases?

He could pick base 9 to 16 or something and with fractions and it could get crazy :(

Last edited:
Yes. That works too if you are up to following the rules of base arithmetic.

I think I'll stay with base 10 though thank you.

Good luck.

## 1. What are number bases and why do we change them?

Number bases refer to the number system used to represent numbers, such as decimal (base 10), binary (base 2), and hexadecimal (base 16). We change number bases to make it easier to perform calculations, simplify complex numbers, and to better understand how numbers are related.

## 2. How can we convert numbers between different bases?

To convert numbers between bases, we use a process called "base conversion". This involves dividing the number by the base we want to convert to, and then using the remainder as the new digit. This process is repeated until the number becomes 0. For example, to convert 10 (decimal) to binary, we divide 10 by 2 to get 5 with a remainder of 0. Then, we divide 5 by 2 to get 2 with a remainder of 1. Finally, we divide 2 by 2 to get 1 with a remainder of 0. Therefore, the binary equivalent of 10 is 1010.

## 3. What is the significance of the base 2 in binary numbers?

The base 2 in binary numbers represents the number of digits used to represent a number. In binary, we only use two digits (0 and 1) whereas in decimal, we use 10 digits (0-9). This makes binary numbers much more compact and efficient for computers to use, as they can easily represent numbers using only two states (on/off or 0/1).

## 4. Can we convert numbers between any two bases?

Yes, we can convert numbers between any two bases. However, the process may become more complex for bases that are not commonly used, such as base 8 (octal) or base 16 (hexadecimal). It is important to understand the base conversion process and have a good understanding of both bases to successfully convert numbers between them.

## 5. How does changing number bases relate to computer programming?

In computer programming, binary is the most commonly used base for representing numbers. This is because computers use binary digits (bits) to store and process data. Therefore, understanding how to convert between binary and decimal numbers is crucial for programming and working with computers.

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