 So there's one special and interesting case of multiplication which is going to be actually multiplied by whatever the base is. So let's take a closer look at that. So let's say I want to multiply 4 times a number that's written in base 4. So this is 4 times 2, 1, 3, base 4. And so I'll start out the same way. We'll go ahead and write down a number using the place value chart, and we'll keep in mind that this is really the same as adding 4, 2, 1, 3, base 4s together. So I'll go ahead and write down that addition this way. All right, now what we could do is we could add within each column and then find our subtotals as we've been doing, but let's be a little bit more clever about this. Looking ahead, we know that because we're working in base 4, 4 of anything can be traded for something in the next place over. So that means that I can take these four things here, and very briefly I can treat these as each one of these as its own unit. This is a two thing. I don't know what the name is. I don't really care. It doesn't make a difference. But I have four of them, which means I can trade these for an equivalent amount in the next place over. So four of these things can be traded over for one of whatever is in the next place over. So four 2s give me a 2 in the next place over. Likewise, four of anything, four of these will give me one in the next place over, and four of these will give me the same amount in the next place over. So I can trade four over, trade four over, trade four over, and then I do want to indicate that there is a last place there. So I'll put a zero in that last place, and then finally write down my number in base 4, 2, 1, 3, 0, base 4 as my product. And here's the thing that's worth noting. When I multiply a number by the base, what I get is I get the same digits, except in this case I've tacked a zero onto the end. And the reason for this is when I collect base 4 of these things, I get the same amount in the next place over, and that frees up this one space at the end where we have to indicate that there is none of that particular unit present by writing a zero.