00:01
Okay, so the decimal system is considered a base 10, and we write that as base, while base 1 ,0, and we say, well, right, that is considered that base 10, right? but why is because we are grouping things in powers of 10.
00:15
So for a number, let's just write a number, let's say something like 276.
00:22
Well, what is 276? that's 200s plus 710s plus 6 ones.
00:29
And we literally say 2007t, that ty is short for 10, and then 6.
00:36
So 276 is 200, 710s, and 6 ones.
00:40
But we could write a number, something like maybe 101, maybe 101.
00:49
Okay, well, if we're in base 10, again, this is 100 and 1, right? we say 1001.
00:56
But we could maybe be in a different base system.
00:59
Like, let's say, base 2.
01:01
Now, in a base 2 system, our place values are now powers of 2.
01:07
So if this is in binary or base 2, this would be, while looking at a place value chart here, so let's say each box here, if we're in base 10, well, then every box is powers of 10.
01:22
If we're in base 2, then this right most box is still 1, but then we would have 2 ones, would make 2.
01:30
And then two twos would make four and we kept going two fours would make eight and two eight would make sixteen and so on so a number like one zero one is literally saying one four no twos and one one one four plus one so one zero one well that's equivalent to five right one zero one is five if this is in base two so one zero one base two is equivalent to five in base ten and really one zero, well, one zero, we know is 10.
02:05
That's 110 and no ones.
02:07
But we're in base two, well, one zero is one two and no one.
02:11
So one zero, that is equivalent in base two.
02:16
That is going to be equivalent to two.
02:18
If we're in base three, well, it's the same thing.
02:21
But now our boxes, our place values are now powers of three.
02:26
So the right most box is still one...