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I now want to show you that the standard algorithm for multiplying numbers can also be use it's not just limited to base ten it can also be used frankly can be used at any base but we're going to do it in base two and base two is especially fun because you essentially have to only know your multiplication tables through one so you just have to know that zero times zero is zero one times zero is zero and that one times one is one and then you're ready to go you're ready to multiply in base two so let's do that so let's say we have let's take let's say we take nine so let's see nine it's going to be one eight zero fours zero twos and one so this is nine right over here represented in base two and let's say we were to multiply that times let's say we were to multiply that times seven so we should obviously if we know our multiplication tables we should get 63 so seven is one i channel to zero it was seven would be one one one but that that's a little bit boring so let's let's instead do let's do nine times five which we know should be 45 so this is one for no twos and one one so four plus one is going to be five so this is nine times five and we're doing it in base two so once again same algorithm and actually before I do it I encourage you just pause the video and try to use the same algorithm that you've used for for base ten multiplication use the same algorithm here and let's see if we actually do get that 9 times 5 is 45 so I'm assuming you've had a go at it let's work through it together so let's start right over here in the ones place so we multiply 1 times 1 is 1 1 times 0 is 0 1 times 0 is 0 1 times 1 is 1 then we can go to the twos place and since we're multiplying all of this times the twos place we can throw a 0 right over here but of course 0 times each of these is just going to be a bunch of 0 so we you know 0 times 1 zero zero times zero zero zero times zero zero zero times 1 is 0 so I really didn't have to write that but I'm just doing it so that you see that I'm using the standard algorithm and then we go to the for is place and since we're in the fourth place let's put some zeros here so zero zero we're essentially figuring out where we're essentially talking about I'm certain number fours not a certain number of ones so one times that is just going to be 1 0 0 1 and now we're ready to add now we are ready to add so 1 plus a bunch of zeros is 1 a bunch of zeros that's going to be 1 1 plus a 0 bunch of zeros is 1 zeroes and 1 and we're done and obviously if we had a but if we had more than 1 1 in any of these places right over here then we might have had to carry a 1 but we saw that when we added when we added numbers in binary but let's actually verify that this is the number that we would expect it to be remember this right over here is the ones place so let's see this is ones fours let me write it down this is ones this side ones twos fours 8 16 and 32 s so we have so we have 1 32 so it's going to be 32 plus 1 8 I don't do it we only have to do this for ourselves because we're so used to thinking in base 10 if you were thinking in base 2 you'd say oh I know what this number is and you would have some name for it other than 45 because 45 the name essentially is kind of a base 10 name and we'd probably have better names in terms of base 2 someone actually should do that that would be a fun that would be a fun you would call well we would call this well that would be that would be a fun project so see with 32 plus 8 plus 4 plus 4 plus 1 plus 1 which is indeed equal to 45