Binary: How To Convert Base-10 To Base-2 Binary - Part 1

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1. Step 1: Meet Mr. Ford:

   Hi this is Mr. Ford from mrfordsclass.com and in this presentation I am going to show you how to convert normal base 10 numbers, that's the numbers that we're used to, that we're taught in kinder garden on through school, to a binary format.

2. Step 2: It's easy to convert:

   Now, depending on how you learn this, if you look in textbooks, I find it to be very complicated and very not user-friendly. This is a very easy way to be able to convert between the two. I hope you enjoy it, I hope it helps you out.

3. Step 3: Create your table:

   The first thing you have to do is create your table. You start with your numbers up top and then you draw your little lines down. You start with the number one and then we double it. So one plus one is two. Double two. Two plus two is four. Four plus four is eight. Eight plus eight is sixteen. Sixteen plus sixteen is thirty-two. Thirty-two plus thirty-two is sixty-four. Sixty-four doubled is one-twenty-eight. One-twenty-eight plus one-twenty-eight is two-fifty-six and two-fifty-six plus two-fifty-six is five-twelve. Now you might be recognizing some of these numbers, like one-twenty-eight, two-fifty-six and five-twelve as also being the size of memory, ram sticks. This is not a coincidence; remember the computer works via binary. And this is how we count binary which is also how memory stick are rated.

4. Step 4: Making conversions:

   Okay, so, let’s actually do some conversion here. If I want to have the number thirty-two, what I do is I look for the number that’ll go into it. Meaning, which of these numbers will go into thirty-two. Well, in our case, thirty-two will go into the number thirty-two. So we put a one here and then we put zeros at the end part because none of these other numbers are needed. Okay, now let’s say I want the number five. Well, can this go into five? No. two-fifty-six, no, blah-blah-blah-blah-blah. The first number that can go into five is the number four. So I put a one here because four goes into five. So we have five, we put a four in there, we have one left. Can two go into one? No, so we put a zero. Can one go into one? Yes. So, we have a four and a one. Four plus one is five.

5. Step 5: A different approach:

   Let’s show you that in a different way. Let’s say I want the number ten. Which number is the first number that can go into ten? Well, sixteen can’t, but eight can. So eight into ten, what do we have? Eight, nine ten; we have two left that we have to put in somewhere. Can four go into two? No. Can two go into two? Yes, we’re left with zero. So, for the number ten, it’s one, zero, one, zero in binary.

6. Step 6: A more difficult example:

   Let’s go with a harder number. Let’s say we want to go with the number sixty-three. Can sixty-four go into sixty-three? No. So there’s nothing there, can thirty go, thirty-two go into sixty-three? Yes. Now here’s a little helpful hint. We could do the math, we could do sixty-three minus thirty-two minus blah-blah-blah-blah-blah-blah-blah, but there’s an easier way to do this. Sixty-three is the number right before sixty-four which means that everything before-hand added up will equal that number. So sixty-three, one at the thirty-two, one sixteen, one at eight, one at four, one at two, one at one. This added up will equal sixty-three. Because if we wanted sixty-four, we’d put the one here and the zeros back here. So, everything added up is going to be sixty-three.

7. Step 7: Clearer than mud:

   So, once again, in case I made that as clear as mud, if you want the number right before your big category, let’s say I want one-twenty-seven, it would be everything checked from here over. If I wanted two-fifty-five, it would be everything here over.

8. Step 8: What goes into what?

   Let’s try one more. Let’s say I want the number seven. Let me show you how this works. I want the number seven. Well, eight doesn’t go into seven, but four does. Four, five, six, seven. Does two go into three? Yes. So I have three, I just took away two, I’m up to one. Does one go into one? Yes. So, seven is the number right before eight, so all those are checked.

9. Step 9: Thanks for watching:

   Hope this helps you out. This is not that hard if you set up your table. And remember, you don’t have to memorize the numbers up here. Just know how they work. You start at one. One plus one is two, two plus two is four, four plus four is eight, eight plus eight is sixteen, sixteen plus sixteen is thirty-two, ad nauseam. And you can go pretty much to infinity here with your numbers. So I hope this helps, it’s not everything you need to know about binary out there, but it is a good beginning, a good grounding level so you can build off this knowledge.

Thanks for watching our video Binary: How To Convert Base-10 To Base-2 Binary - Part 1 For more how to videos, expert advice, instructional tips, tricks, guides and tutorials on this subject, visit the topic Math.