Converting Decimal to Different Base

In this post, I said that if you wanted to convert number from different base to decimal we could use table. Well, I’m sorry that I was wrong because I’ve just remembered that we use table to convert decimal to other bases. There may be table for converting to decimal but I haven’t known yet.

In the image below, I convert 27 base 10 to binary.

Converting 27 to Binary

Another example below, I convert 27 to base 3.

Converting 27 to Base 3

2 + 2 = ?

Today’s assignment in Blogging 101 is about writing with prompt. I’ve made one post for that assignment but I want to write again.

In today’s assignment post, the prompt example is, “Two plus two equals four: yes or no?”

Reading that prompt, I remember Sujiwo Tejo, an Indonesian artist who is also interested in math. He once said, “Math is not exact science. It’s a science of agreement. You can say 1 + 1 = 2 only if you agree to use base 10. If you use different base, the result can be different.”

What is base? You can read this if you want to learn about it.

I will try to explain about base or numeral system. The numeral system we usually use is base 10 or decimal. It consists of ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. There is also base 2 or binary which only consists of two numbers: 0 and 1. Base 3 consists of three numbers: 0, 1, and, 2.

So, 2 + 2 = 4 in decimal. What if we use base 3? Let’s see how numbers are written in base 3: 0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, …. From this, we can see that in base 3, 2 + 2 = 11

In base 4, numbers are written as 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, …. So, 2 + 2 = 10 in base 4.

What if we want to convert number from different base into decimal? Well, you can use a table (not the table you see here) but I can’t upload the table. Maybe later (procrastination alert!!!). Other method is like this I explain below.

For example, if I want to convert 111 base 2 into decimal, it will be

111₂ = 1 x 2² + 1 x 2¹ + 1 x 2⁰ = 7

Another example, converting 23 base 5 into decimal will be like

23₅ = 2 x 5¹ + 3 x 5⁰ = 12

It’s been a long time that I haven’t studied math. How is my explanation? Is it understandable or confusing? Sorry, if you’re confused.