Decimal to Binary Decimal to HEX 1. How is 1810...

Decimal to Binary & Decimal to HEX 1. How is 1810 represented in binary (base 2) and hex (base 16)? Show your work. (2) Binary - Base 2 Chart (0,1) Hex - Base 16 Chart (0-9,A-F) 128 64 32 16 8 4 2 1 268 mil+ 16mil+ 1mil+ 65k+ 4096 256 16 1 2. How is 2610 represented in binary (base 2) and hex (base 16)? Show your work. (2) Binary - Base 2 Chart (0,1) Hex - Base 16 Chart (0-9,A-F) 128 64 32 16 8 4 2 1 268 mil+ 16mil+ 1mil+ 65k+ 4096 256 16 1

Transcript

00:02 So this problem asks us to do a bunch of conversions.

00:06 So the main part of the conversions require us to use the binary table and the hex conversion groups.

00:13 So the first part is to convert 250 into binary.

00:17 So in order to do that, what we're going to do is find the biggest number from the binary table that we can subtract from 250.

00:24 So that'd be 128.

00:25 So 250 minus 128, which gives you 122.

00:31 And then you take 122 minus the biggest number so 64 which gives you 58 and you go so on so you end up with going with one one one one and then that gets you all the way down to a value of 10 so after you subtract all the way from 16 you end up with 10 and then you subtract from 8 so that gives you another one in the spot for 8 and that so you you're left with two.

01:03 So you can't subtract from four, but you can't subtract from two, and that'll give you a value of zero.

01:09 So this right here, 11111, 101 is your binary number.

01:13 To convert this in the hex, we're going to use these right here.

01:17 So you're going to go 8, 4, 2, 1 for every group of 4 numbers in the binary values.

01:23 So here you're going to take the sum of 2 and 1 in the first group.

01:27 So 2 and 1, that gives you 3.

01:29 In the second group, take the sum of all numbers, and you end up with the value of 5.

01:32 15.

01:33 Since hexadecimal can only go up from 0 through 9 and then you have to use abc, you're going to have to write 3 and then a starts at 10.

01:45 So if you just go on, you end up with f for 15.

01:50 So your hexadecimal number is 3f.

01:57 So now if we keep going.

01:58 The next problem asks us to convert the binary into decimal again.

02:03 So we're going to do this, you can basically set it up.

02:05 So it's 2 .a .7th, 2 .8 .6th, 4th, 2nd, 1st, and 0th.

02:16 So based on this, if you just multiply the numbers above where they are.

02:21 So for this example, you would go 2 raise to the 6th plus 2 to the 5th plus 2 raise to the 4th, not 2 to the 3rd, plus 2 raise to the 2nd, and plus 2 raise to the 0th.

02:33 So you end up with the value of 117 for your decimal number.

02:39 Now you want to convert this into hex.

02:42 So this is binary.

02:44 So you're going to do the 8421 trick again.

02:46 So 8421, 8421.

02:49 So you take the sum of this right here, but not two.

02:53 So 8, 4 and 1, so that results in the value of 13.

03:00 And if you take the sum of these two, not these two, then you end up with the value of 12.

03:04 So again, you want to use the abc technique.

03:08 So that gives you d and c for your hexadecimal value.

03:14 Now to convert a and b into binary and decimal, what you can do is set up a and b.

03:20 So a and b in the 841 trick is going to be 10 and 11.