How Do You Convert Numbers from Base 8 to Base 2?

[multiix]

Hi guys I'm not sure if this is the right place to post, so if its not please redirect me.

We are learning Number system conversions and I am having trouble converting anything other than base 10 to other bases. Ex base 8 to base 2.
I tried converting say 456 base 8 to base 2
This is not a homework question so
If you would like to post a General equation please go ahead. I just want to understand how to do this
Step by step.

Equations:
I'm currently writing things in the form Q and R chart

Work:
456 I try converting that to base 10, I get 302 then I divide by 2, I get 151 remainder 0 but I'm not sure if this is the correct way because I remember my teacher dissecting the 456 into 3 different number 4,5,6 and dealing with them separately. Also if I don't know if the 151 that I got is base 10 or 8

Please Help. Thank you

 

[Integral]

You must do your arithmetic in the correct base. Do do your conversion you must do base 8 arithmetic.

Another way would be to convert the base 8 to base 10 (using base 10 arithmetic) then convert the base 10 number to binary.

 

[multiix]

Oh ok. I got it that way. Thank you :)
100101110

Is there any other way of doing it without converting to Base 10 first? Not that it's hard

 

[Integral]

You can go directly between any 2 bases as long as you use appropriate arithmetic.

 

[DeeNos]

Hi there,

I understand your struggles with number system conversions. It can be confusing and overwhelming to learn at first, but with practice and a clear understanding of the process, you will be able to convert numbers easily.

Firstly, it's important to understand the base system. In base 10, we use 10 digits (0-9) to represent all numbers. In base 8, we use 8 digits (0-7) and in base 2, we use 2 digits (0-1). So when converting from one base to another, we have to keep this in mind and make sure we are using the correct digits.

Now let's look at how to convert from base 8 to base 2. As you mentioned, your teacher dissected the number 456 into 3 different numbers (4, 5, 6) and dealt with them separately. This is the correct approach.

Step 1: Convert each digit from base 8 to base 10.
4 base 8 = 4 base 10
5 base 8 = 5 base 10
6 base 8 = 6 base 10

Step 2: Convert each base 10 number to base 2.
4 base 10 = 100 base 2
5 base 10 = 101 base 2
6 base 10 = 110 base 2

Step 3: Combine the converted numbers to get the final answer.
456 base 8 = 100101110 base 2

So to summarize, when converting from base 8 to base 2, you have to first convert each digit from base 8 to base 10, and then from base 10 to base 2. You can also use the general equation (Q and R chart) to help you with the process.

I hope this explanation helps you understand the process of converting numbers in different bases. Keep practicing and you will become more comfortable with it. Good luck!