I was browsing Reddit this morning and happened across a conversation about binary (…you know, the weird language of 0’s and 1’s? I’ve known *what* binary is for a long time but up until today I never understood how it worked, in the sense of how do you represent a number – say, 300 – in 0’s and 1’s. But thanks to a very clear explanation in that Reddit conversation, I think I’ve finally got it.

When you write the number 300 you are using *base 10*. There are zero 1’s, zero 10’s, and three 100’s. Every place value bumps earlier place values to the right.

When you represent the same value in *base 2*, or binary, you start with 1’s, then 2’s, then 4’s, then 8’s, then 16’s, and so forth. It would show up as 100101100 because you have zero 1’s, zero 2’s, one 4’s, one 8’s, zero 16’s, one 32’s, zero 64’s, zero 128’s, and one 256’s. Get it? Remember that each new place value bumps previous place values to the right, so your 1’s is the furthest place value to the right and the 256’s is the furthest place value to the left.

It’s so easy!


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