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]]>When it comes to your algorithm for converting a decimal number to a binary number, I had a moment this morning when I learned something. I often teach base-5 to my future teachers, so I am aware of the division procedure to convert a decimal number to base-5 (divide by decreasing powers of 5).

For example, if we want to convert 176 to base-5, we first divide by 125, then by 25, then by 5 – keeping track of the remainders to get (1201)_5. Notice that your algorithm won’t work (easily) for base-5 (can you see why we would use division instead of subtraction in base-5?). Your subtraction procedure intrigued me, and I wondered why you didn’t use division – then I realized that in binary you either divide by the power of 2, or you don’t! How beautiful! Division is not needed because either we get digit 1 or we get digit 0 – there are no other digits like we have in base-5.

I also find it interesting that you would do the mental arithmetic in base-10 – this is often how I teach my teachers as well! It is interesting that base-10 is so ingrained in our body that it is difficult to truly part with when learning another base system. I wonder if anyone has raised children in binary! Now THAT would be interesting to hear about ðŸ˜€

As you teach more you will find that the “damn good feeling of reward” is pretty vital to most – this, I think, makes us remember certain teachers. We can recall when we were given opportunity, and when we were rewarded for it. Of course, it is well-known that this “feeling of reward” leads to more motivation! Ideally, it is a beautiful circle of learning.

Looking forward to reading more!

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