00:01
In this problem, our job is to do the following conversions.
00:03
In part 1, to convert from hexadecimal to binary.
00:06
And in part 2, to convert from various bases to decimal.
00:11
So to do the first conversions, we will start out by writing down each of the hexadecimal digits in their binary form.
00:29
0, of course, is four 0s.
00:33
1 is 0, 0, 0, 1.
00:37
2 is the row 0, 1, 2, because we have a 1 in the 2's place and a 0 in the 1's place.
00:44
And that pattern continues.
00:49
Excuse me, i'm getting 1 ahead here.
00:52
That's 4.
00:53
Let's go back and do 3 before we do 4.
00:55
There we go.
01:01
So writing down each of the hexadecimal digits in terms of binary will help us along the way.
01:15
So here's the pattern for 0 through 7.
01:17
And then 8 through, now of course when we hit 10 we use an a for 10 and a b for 11 and so on.
01:29
We now have those same values but with a 1 in the leftmost place.
01:40
And so finally we have our last 4, c, d, e, and f representing 12 through 15.
02:00
All right, so we've taken a little time to do that conversion because that will help us with each of the three parts in number one.
02:08
So the first of those that we need to work on is the hexadecimal number 2a7f.
02:18
Let's come down here where you can still see those.
02:22
So to convert 2a7f from hexadecimal, we will simply convert each of those hexadigits one at a time into binary using the chart we've just written down above.
02:47
So we we have the a as 1, 0, 1, 0.
02:51
Now, it's not necessary to put a little line in here, but you certainly can if it helps you keep it straight.
02:58
It's going to have 16 bits in all.
03:02
7, we've seen, is 0, 1, 1, 1.
03:08
And then finally, f is 4, 1s.
03:15
So our first conversion from hexadecimal to binary looks like this.
03:20
And we don't have to put a little 2 there, but we can put a little 2 there just to remind us that's binary.
03:26
All right, there's our first conversion.
03:28
We're going to do the other two the same way.
03:30
Let's make some room for those.
03:33
The second example asks us to write ff00, the hexadecimal form in binary.
03:44
And so we simply have the conversion for f and then another f and then zero, and then another zero.
03:56
So here's the answer for part b in binary...