Bases - What are They? (Part 3) How to change base 2 numbers into base 10
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This short lesson is a continuation of the posts at:
In those lessons, we talked about what bases are, what they’re used for, and how to change numbers from base 10 to base 2 (easy!)
It’s even easier to change numbers from base 2 into base 10.
When you read a number in base 2, you simply have to add the columns together that have a 1 in them, and ignore the columns with a 0 in them.
In the number 111(base 2) there is a 1 in the fours, twos, and ones columns. Simply add 4, 2, and 1 to get the base 10 value, which is 7.
The number 10110 has a 1 in the sixteens column, another in the fours column, and another in the twos column. So add 16 + 4 + 2, to give you 22, base 10.
You have to admit that’s pretty easy.
What would the number 110101 (base 2) be, in base 10?
Answer it in a comment, if you like.
Tags: convert base 2 to base 10
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Comment by Steph
Let’s see … 110101 in base 2 — converted to base 10 — is 32+16+4+1=53??
I remember being briefly exposed to bases in school … but no one really explained them or thought to mention why they were important. of course this was back in the day when computers weren’t a part of most people’s everyday experiences.
Thanks for posting the clear, informative articles.
Professor Homunculus sez:
Yup, you nailed it right on the bean. And thanks for your nice comment.