1 00:00:04,670 --> 00:00:07,590 So if you've been following through the previous video, 2 00:00:07,590 --> 00:00:09,750 we talked about the binary number system. 3 00:00:09,750 --> 00:00:12,640 You may actually have made the following two observations. 4 00:00:12,640 --> 00:00:18,140 Firstly, converting from decimal To binary tedious once you get up above four bits or 5 00:00:18,140 --> 00:00:19,470 eight numbers in the range 0 through 15. 6 00:00:19,470 --> 00:00:22,890 And binary numbers have a lot of numbers have a lot of digits and writing and 7 00:00:22,890 --> 00:00:27,250 speaking them is both boring and, more importantly, error prone. 8 00:00:27,250 --> 00:00:30,660 So as a result, programmers very often use hexadecimal instead. 9 00:00:30,660 --> 00:00:36,070 Hexidecimal, or as it's usually called X is basic 16 and because 16 is 10 00:00:36,070 --> 00:00:41,510 an exact power of two, converting between binary and hex is actually quick and easy. 11 00:00:41,510 --> 00:00:45,580 Now once again, I'm gonna point out you don't need to understand this section 12 00:00:45,580 --> 00:00:47,800 in order to complete the rest of the course. 13 00:00:47,800 --> 00:00:51,790 So don't feel that if you haven't got a good understanding of this section that 14 00:00:51,790 --> 00:00:54,900 The next sections are going to get worse because that's not the case, but 15 00:00:54,900 --> 00:00:58,390 the thing here is that our discussion of binary wouldn't be complete 16 00:00:58,390 --> 00:01:00,310 without covering hexadecimal. 17 00:01:00,310 --> 00:01:01,850 So if you want to skip the rest of this video, 18 00:01:01,850 --> 00:01:03,600 and move on to the next section then please do. 19 00:01:03,600 --> 00:01:06,790 And we'll get back to regular Python programming. 20 00:01:06,790 --> 00:01:07,330 Look. You can 21 00:01:07,330 --> 00:01:10,170 also come back to this section once you've mastered Python, and 22 00:01:10,170 --> 00:01:12,380 you no longer having to remember loads of new things. 23 00:01:12,380 --> 00:01:13,330 So continuing on. 24 00:01:13,330 --> 00:01:16,750 Hex has got a number of advantages over binary. 25 00:01:16,750 --> 00:01:22,210 Firstly hex numbers are much shorter and that makes writing them a lot easier. 26 00:01:22,210 --> 00:01:26,530 For the number 0 through 255 can be written in just two hex digits and 27 00:01:26,530 --> 00:01:30,940 the number 0 to 65,535 With just four hex digits. 28 00:01:30,940 --> 00:01:34,970 The other thing is that working in hex provides a convenient way to remain close 29 00:01:34,970 --> 00:01:36,210 to the underlying binary. 30 00:01:36,210 --> 00:01:39,550 And this can be very useful when you're actually dealing with memory addresses, or 31 00:01:39,550 --> 00:01:41,970 operations that work on individual bits. 32 00:01:41,970 --> 00:01:45,730 And that's like using and or an xor, which we saw in the previous video. 33 00:01:47,210 --> 00:01:48,260 So moving on to the next slide. 34 00:01:48,260 --> 00:01:53,550 Working in base 16 means that we actually need a way to represent the 16 digits 35 00:01:53,550 --> 00:01:58,500 from 0 to 15 in the same way that, in base 10, we had the digits from 0 to 9. 36 00:01:58,500 --> 00:02:02,230 So rather than create 6 more digits to represent 10, 11, 12, 13, 14, and 15, 37 00:02:02,230 --> 00:02:06,820 th symbols A to F are actually used instead. 38 00:02:06,820 --> 00:02:11,000 Now each hex digit represents four binary digits called a nibble. 39 00:02:11,000 --> 00:02:13,790 And seriously, I know it's a weird name but that's what they're called. 40 00:02:13,790 --> 00:02:18,780 So to represent an 8 bit-byte, we actually use two hex digits. 41 00:02:18,780 --> 00:02:21,840 So let's go back now and change the program that we wrote 42 00:02:21,840 --> 00:02:24,690 in the previous video to print out the numbers in hex. 43 00:02:24,690 --> 00:02:27,260 So I'm gonna shoot back over to the Intelligo, so 44 00:02:27,260 --> 00:02:29,180 a simple change of we'll just briefly type it in again. 45 00:02:29,180 --> 00:02:34,720 I've got a new for, so for i in range 17, and we'll 46 00:02:34,720 --> 00:02:41,830 do our print(" 47 00:02:41,830 --> 00:02:51,130 in hex is ".format) 48 00:02:52,730 --> 00:02:55,990 Note that I use x here to represent hex and hot h. 49 00:02:55,990 --> 00:02:57,070 So, I've actually run this. 50 00:02:58,950 --> 00:03:02,220 You can see the numbers and the cross pointing value in hex. 51 00:03:02,220 --> 00:03:04,510 So, 0 through nine is equivalent to decimal. 52 00:03:04,510 --> 00:03:09,200 But once we get to 10, notice how instead of 10 we went to oi, 11 is ob. 53 00:03:09,200 --> 00:03:12,160 12 is [INAUDIBLE] and so on, right through to 16, and 54 00:03:12,160 --> 00:03:14,660 16 effectively becomes 10, 1, and 0. 55 00:03:14,660 --> 00:03:19,480 So [INAUDIBLE] partially uses the letter B in the format stream to represent binary. 56 00:03:19,480 --> 00:03:23,370 We saw that in the previous video when I used X as I pointed out on the screen, 57 00:03:23,370 --> 00:03:26,730 not H to represent X If you want to extend the range to 256, 58 00:03:26,730 --> 00:03:30,440 you can actually see how counting in hex works. 59 00:03:30,440 --> 00:03:33,470 So adding one then carries over to the next column as a source. 60 00:03:33,470 --> 00:03:38,260 So for example, 1F is 116 plus 15 units, which is 31. 61 00:03:38,260 --> 00:03:42,670 20 and hex is two 16s, and no units, which is 32. 62 00:03:42,670 --> 00:03:46,200 Now, if a hexadecimal number contains one of the letters a to f, 63 00:03:46,200 --> 00:03:49,130 it's actually obviously easy to see that it's a hex number. 64 00:03:49,130 --> 00:03:52,180 But however, the number 20 is not obviously hexadecimal. 65 00:03:52,180 --> 00:03:56,630 So if we're dealing with hex numbers, we need some way to identify them as such. 66 00:03:56,630 --> 00:04:01,520 Python along with many other languages allows or uses the prefix 0x to actually 67 00:04:01,520 --> 00:04:05,930 identify a hex number as the following simple program we're about to demonstrate. 68 00:04:05,930 --> 00:04:10,630 So I'm gonna type in that so obviously we can type x=20. 69 00:04:10,630 --> 00:04:12,860 Exit 20, but based on that, 70 00:04:12,860 --> 00:04:17,630 you wouldn't know whether you meant 20 decimal or 20 hex. 71 00:04:17,630 --> 00:04:20,390 But if I type in 0X 20, that actually 72 00:04:20,390 --> 00:04:24,700 tells Python that we want to actually type in the hex number for 20. 73 00:04:24,700 --> 00:04:32,210 So y equals 0X0A, and then we could do a print X, print Y. 74 00:04:32,210 --> 00:04:33,230 Let's do a modification. 75 00:04:33,230 --> 00:04:36,790 Print X times Y So let's run that. 76 00:04:36,790 --> 00:04:39,540 And you can see the results there. 77 00:04:39,540 --> 00:04:41,920 First one, 20, which is actually 32. 78 00:04:41,920 --> 00:04:44,900 So we're asking it to print out the decimal equivalent. 79 00:04:44,900 --> 00:04:47,800 And y, which was 0x0a, the equivalent is 10. 80 00:04:47,800 --> 00:04:52,330 And the last one, multiplying them together So it's basically 32 by 10 81 00:04:52,330 --> 00:04:57,010 effectively, or 20x multiplied by [INAUDIBLE] X, and 82 00:04:57,010 --> 00:05:01,180 that's 320 as a decimal number, is the actual total in decimals. 83 00:05:01,180 --> 00:05:02,980 And I didn't point it out in the previous video, but 84 00:05:02,980 --> 00:05:07,830 you can actually specify binary literals using the prefix ob. 85 00:05:08,980 --> 00:05:14,580 So we could do something like 0b00101010 To actually print out a value in binary. 86 00:05:14,580 --> 00:05:18,260 So if we run that, that would be the binary equivalent, and or in decimal, 87 00:05:18,260 --> 00:05:21,310 42 is equivalent of that binary number there. 88 00:05:21,310 --> 00:05:22,360 Now the other thing to point out, 89 00:05:22,360 --> 00:05:24,750 is that leading zeros are not actually necessary either. 90 00:05:24,750 --> 00:05:26,810 So in other words, we could have done the same thing here, 91 00:05:26,810 --> 00:05:28,070 we could have just removed those two. 92 00:05:29,570 --> 00:05:30,900 Run it. 93 00:05:30,900 --> 00:05:32,480 We've got exactly the same value. 94 00:05:32,480 --> 00:05:33,740 Hexadecimal addition and 95 00:05:33,740 --> 00:05:38,010 subtraction can actually be performed just like decimal addition and subtraction. 96 00:05:38,010 --> 00:05:42,040 But with that said there's very few people these days who actually think in hex. 97 00:05:42,040 --> 00:05:45,720 Now it use when we didn't have modern programming languages and compilers 98 00:05:45,720 --> 00:05:49,570 that we have these days programmers often work with machine code or assembler And 99 00:05:49,570 --> 00:05:53,270 you can actually find programs he thought encountered effectively in hex, but 100 00:05:53,270 --> 00:05:54,690 this is becoming rarer. 101 00:05:54,690 --> 00:05:58,170 I actually, myself, developed games back in the day and 102 00:05:58,170 --> 00:06:03,540 I didn't actually have an [INAUDIBLE] so I actually had to deal with hex and 103 00:06:03,540 --> 00:06:08,070 I had to understand how to actually calculate numbers in hex but 104 00:06:08,070 --> 00:06:09,880 also [INAUDIBLE] what they actually meant in their values. 105 00:06:09,880 --> 00:06:11,810 So, It's something that you can certainly learn, but 106 00:06:11,810 --> 00:06:13,900 these days it's not something you really need to. 107 00:06:13,900 --> 00:06:15,680 So let's swing back now on to the next slide. 108 00:06:17,650 --> 00:06:21,720 So in this calculation I'm gonna show you 8A take 4E. 109 00:06:21,720 --> 00:06:23,650 So 8E requires us borrowing from the next column. 110 00:06:23,650 --> 00:06:24,890 So we actually borrow 16. 111 00:06:24,890 --> 00:06:28,840 Now, at this point, most people would probably add 16 to 10. 112 00:06:28,840 --> 00:06:30,740 Or A and Hex to give 26. 113 00:06:30,740 --> 00:06:36,400 So, taking away E which is 14 leaves 12 and so we have c in the first column. 114 00:06:36,400 --> 00:06:38,920 Seven take four leaves three in the second column. 115 00:06:38,920 --> 00:06:42,290 So, the answer is three c in hex or 60 in decimal. 116 00:06:42,290 --> 00:06:45,110 So if you had to perform addition and subtraction in Hex 117 00:06:45,110 --> 00:06:48,750 without using a calculator, it's natural to convert the digits to decimal. 118 00:06:48,750 --> 00:06:51,850 Now the standard calculators that come with Windows, Linux and 119 00:06:51,850 --> 00:06:56,070 the Mac all have an advanced mode that can perform Hex arithmetic, and 120 00:06:56,070 --> 00:07:00,370 you see how easy it is to do it in Python, so Now frankly there's no real reason for 121 00:07:00,370 --> 00:07:03,480 risking errors by performing these calculations yourself. 122 00:07:03,480 --> 00:07:05,040 So in Windows there's a couple of options. 123 00:07:05,040 --> 00:07:07,580 There's either a scientific option under the view menu or 124 00:07:07,580 --> 00:07:10,640 in Windows 10 it's got a programmer mode in the settings menu. 125 00:07:10,640 --> 00:07:13,790 On the Mac, there's a programmer mode under the view menu. 126 00:07:13,790 --> 00:07:18,180 And under Ubuntu Linux, there's also a programmer mode under the mode menu. 127 00:07:18,180 --> 00:07:20,910 So there's a few options if you do actually wanna go in and 128 00:07:20,910 --> 00:07:22,370 check out the calculator and try it out. 129 00:07:22,370 --> 00:07:26,460 It's actually quite useful to do that just to sort of see how it all works, 130 00:07:26,460 --> 00:07:29,810 but again it's not something you need to understand fully yourself. 131 00:07:29,810 --> 00:07:31,420 Okay, so moving onto the next slide. 132 00:07:33,180 --> 00:07:35,120 Gonna talk now about Octal. 133 00:07:35,120 --> 00:07:41,350 So Octal have like hexadecimal, Octal is base 8 and uses the digits 037. 134 00:07:41,350 --> 00:07:45,570 As you've probably expected I'd soon assume you now understand binary decimal. 135 00:07:45,570 --> 00:07:50,160 And so representing 255 an octal, we've got three times 64 which is 192, 136 00:07:50,160 --> 00:07:55,570 plus seven times eight which is 56 and that gives us 248. 137 00:07:55,570 --> 00:07:57,910 Then adding seven to give 255. 138 00:07:57,910 --> 00:08:01,500 So adding one to that we carry one from the first to second column 139 00:08:01,500 --> 00:08:04,990 Then carry one again from the second to third column, giving you 400 octal, 140 00:08:04,990 --> 00:08:11,680 which is written as 0 in the lower case o 400, the little o in other words. 141 00:08:11,680 --> 00:08:15,620 So it's usual to use lower case so it's not confused with the digit 0. 142 00:08:15,620 --> 00:08:19,340 So Python will allow an upper case letter O, though But 143 00:08:19,340 --> 00:08:21,140 it's not advisable to actually do that. 144 00:08:21,140 --> 00:08:23,910 so octal is really rarely used these days. 145 00:08:23,910 --> 00:08:28,220 One of the few instances that JP could come up with was Linux file permissions, 146 00:08:28,220 --> 00:08:30,120 which are three groups of three bits each. 147 00:08:30,120 --> 00:08:34,559 So it's represents the read, write, and execute permission. 148 00:08:34,559 --> 00:08:37,830 And the first group being the owner's permission, the next group of three bits, 149 00:08:37,830 --> 00:08:39,270 the group's permission, and 150 00:08:39,270 --> 00:08:42,700 finally The last three bits was the permission for all users. 151 00:08:42,700 --> 00:08:48,020 I'm just showing you this on a slide. 152 00:08:48,020 --> 00:08:53,410 So each octal digit corresponds to a three bit binary number, as shown there. 153 00:08:53,410 --> 00:08:55,410 So all seven combinations have been shown, 154 00:08:55,410 --> 00:08:59,780 although not all of them would be used in practice when specifying file permissions. 155 00:08:59,780 --> 00:09:02,730 So the most common permission is to allow read and write access to the owner 156 00:09:02,730 --> 00:09:07,260 of the file And read only to everyone else this will be written as 157 00:09:07,260 --> 00:09:12,110 what's octal number 644 and that will be written as rw-r--r--. 158 00:09:12,110 --> 00:09:15,000 Again, if that didn't make a lot of sense to you, that's okay. 159 00:09:15,000 --> 00:09:18,180 You don't really need to know this, it's more something you can come back to later. 160 00:09:18,180 --> 00:09:20,640 If you're feeling this is a bit overwhelming, don't give up, 161 00:09:20,640 --> 00:09:23,420 move on to the next section if you're finding this a little bit difficult. 162 00:09:23,420 --> 00:09:26,720 Okay, so let's go back to IntelliJ So it's actually time for a challenge. 163 00:09:26,720 --> 00:09:31,660 So we're gonna come up with a challenge to help you understand binary hex and octals. 164 00:09:31,660 --> 00:09:35,280 I'm gonna close down the run window and I'm gonna 165 00:09:35,280 --> 00:09:38,710 comment out this code to to say you've got it there later if you wanna use it. 166 00:09:38,710 --> 00:09:40,910 And I'm gonna paste in what the challenge is. 167 00:09:40,910 --> 00:09:42,290 Gonna paste in there now. 168 00:09:42,290 --> 00:09:43,410 So here is the challenge. 169 00:09:43,410 --> 00:09:47,160 So when converting a decimal number to binary, you look for 170 00:09:47,160 --> 00:09:51,680 the highest power of two, smaller than the number, and you put a one in that column. 171 00:09:51,680 --> 00:09:56,220 You then take the remainder and you repeat the process with the highest power. 172 00:09:56,220 --> 00:09:57,360 Putting a one in it. 173 00:09:57,360 --> 00:09:58,700 Into the remainder. 174 00:09:58,700 --> 00:10:00,110 And is zero otherwise. 175 00:10:00,110 --> 00:10:03,370 And you keep repeating until you've dealt with all the powers down to two. 176 00:10:03,370 --> 00:10:04,810 That is one in other words. 177 00:10:04,810 --> 00:10:07,690 So, what we're going to be wanting to do is writing a program that requests 178 00:10:07,690 --> 00:10:11,430 a number from the keyboard and then prints out its binary representation. 179 00:10:11,430 --> 00:10:13,330 Now, obviously you could use a format string. 180 00:10:13,330 --> 00:10:17,570 But, that's not actually allowed for this challenge because it's too easy. 181 00:10:17,570 --> 00:10:21,240 So, the program should actually cater for numbers up to 65,535. 182 00:10:21,240 --> 00:10:22,740 Other words 2 to the power of 16 take 1. 183 00:10:22,740 --> 00:10:26,170 And that's a hint here, you need integer division. 184 00:10:26,170 --> 00:10:30,590 That's the two slashes for integer division as we've talked about previously 185 00:10:30,590 --> 00:10:33,140 and the modular the percent to get the remainder. 186 00:10:33,140 --> 00:10:38,580 You also need to use the two stars to raise one number to the power of another. 187 00:10:38,580 --> 00:10:41,260 For example 2 * * 8 raises 2 to the power of 8. 188 00:10:41,260 --> 00:10:46,180 And that's an optional extra try avoiding printing leading zeros. 189 00:10:46,180 --> 00:10:51,080 Then once the program is working, modify it to print Octal rather than binary. 190 00:10:51,080 --> 00:10:53,310 So that's is the challenge, see how well you go with it. 191 00:10:53,310 --> 00:10:56,300 Go away and try your best with it and when you're ready to come back and 192 00:10:56,300 --> 00:10:59,640 see what we've come up with, come back and we'll get started on the code. 193 00:10:59,640 --> 00:11:01,230 Pause the video now and I'll see you when you get back. 194 00:11:07,240 --> 00:11:08,230 Okay, so how did you get on? 195 00:11:08,230 --> 00:11:11,650 Hopefully you figured it out, or you managed to get it working, and 196 00:11:11,650 --> 00:11:12,950 let's talk about the solution. 197 00:11:12,950 --> 00:11:16,450 So the way we come up with it was because the highest number we've got to 198 00:11:16,450 --> 00:11:19,100 deal with is one less than two to the power of sixteen, 199 00:11:19,100 --> 00:11:22,620 The first number we need to divide by is 2 to the power of 15. 200 00:11:22,620 --> 00:11:24,140 That is, 32,768. 201 00:11:24,140 --> 00:11:30,770 So we then just keep dividing and printing a zero or a one as appropriate 202 00:11:30,770 --> 00:11:34,650 before repeating with a remainder and the next lowest powers of two. 203 00:11:34,650 --> 00:11:38,290 So we therefore need to loop from 15 down to zero to get the powers of two. 204 00:11:38,290 --> 00:11:42,720 So for our solution, what we're about to do is boot up a list of the powers And 205 00:11:42,720 --> 00:11:45,110 we iterate through the list to print the digits. 206 00:11:45,110 --> 00:11:48,170 So this could all be done in a single loop if you wanted to, then. 207 00:11:48,170 --> 00:11:49,830 So let's actually make a start. 208 00:11:49,830 --> 00:11:50,790 We'll make a bit of space here. 209 00:11:52,930 --> 00:11:57,640 Okay, so we're gonna start by typing powers, create a list. 210 00:11:57,640 --> 00:11:58,480 Powers in empty. 211 00:11:59,890 --> 00:12:03,190 And put for power in range. 212 00:12:06,600 --> 00:12:12,060 15, which is saying this is using the for 213 00:12:12,060 --> 00:12:14,270 loops and stepping and so forth in previous videos. 214 00:12:14,270 --> 00:12:17,380 I'm gonna do powers.append. 215 00:12:17,380 --> 00:12:20,140 [SOUND] To, power. 216 00:12:20,140 --> 00:12:25,430 [INAUDIBLE] So that's actually gonna build our lists. 217 00:12:25,430 --> 00:12:28,720 So in other words, what it should be doing is actually giving us 32,768, 218 00:12:28,720 --> 00:12:31,000 16,384 and right on down to three to one. 219 00:12:31,000 --> 00:12:35,120 I'm gonna actually try that to see that it's working, 220 00:12:35,120 --> 00:12:36,390 by doing a print [INAUDIBLE]. 221 00:12:36,390 --> 00:12:38,530 So let's do that first to make sure it's working. 222 00:12:38,530 --> 00:12:43,890 And you can see that's working so 223 00:12:43,890 --> 00:12:46,740 that's our list which is working containing our powers. 224 00:12:46,740 --> 00:12:47,690 So that's good so far. 225 00:12:48,900 --> 00:12:50,100 So let's continue on. 226 00:12:50,100 --> 00:12:52,730 Now what we want to do is allow the user to talk a number. 227 00:12:52,730 --> 00:12:58,500 So X equal int(input) Please enter a number. 228 00:12:58,500 --> 00:13:04,090 [SOUND] And 229 00:13:04,090 --> 00:13:07,080 what we need to do is actually circle through each of our powers. 230 00:13:07,080 --> 00:13:09,300 So basically eat right through the list now to print the digits. 231 00:13:09,300 --> 00:13:14,800 To do that you can type for power in powers. 232 00:13:14,800 --> 00:13:15,710 We're going through the list. 233 00:13:18,130 --> 00:13:23,390 Print x, x being the number that has been entered by the user, integer division for 234 00:13:23,390 --> 00:13:30,470 power and end equals like so cuz you want it all on the one 235 00:13:30,470 --> 00:13:34,520 line we don't wanna move to the next line and we put x to find the remainder. 236 00:13:36,440 --> 00:13:36,940 Power. 237 00:13:38,300 --> 00:13:41,940 So if we actually run this now, and let's just try to the value ten. 238 00:13:43,230 --> 00:13:47,180 We can see we've got the binary equivalent of one, zero, one, zero binary. 239 00:13:47,180 --> 00:13:52,320 And of course, working that out, we've got a zero in the first digit 240 00:13:52,320 --> 00:13:55,260 The right most bit if you will of the binary number. 241 00:13:55,260 --> 00:13:57,760 We've got a one and that's the value of two there. 242 00:13:57,760 --> 00:14:02,690 Then moving over we've got over here the other one and that's two times two, 243 00:14:02,690 --> 00:14:04,410 which is four times two is eight. 244 00:14:04,410 --> 00:14:06,210 So eight plus two is ten. 245 00:14:06,210 --> 00:14:09,940 So you can see our binary converters actually working just fine. 246 00:14:09,940 --> 00:14:11,710 We mentioned an optional challenge. 247 00:14:11,710 --> 00:14:16,310 So we consider flag once when we hit a non zero value to print. 248 00:14:16,310 --> 00:14:19,320 And we don't actually want to print anything until that flag is set. 249 00:14:19,320 --> 00:14:22,690 The way we can do that is we can modify that here, so power in powers, and 250 00:14:22,690 --> 00:14:28,290 up here we're going to put bit equals x, integer division divided by power. 251 00:14:28,290 --> 00:14:33,450 And then we'll put if bit is not equal to zero 252 00:14:35,380 --> 00:14:38,800 printing is equal to true. 253 00:14:40,580 --> 00:14:44,690 Then here, what we'll do is we'll put if printing [INAUDIBLE] 254 00:14:44,690 --> 00:14:45,250 print, but 255 00:14:45,250 --> 00:14:48,350 instead of doing the division again we'll just use bit at this point 256 00:14:48,350 --> 00:14:51,940 because we've already done the integer division on line 43. 257 00:14:52,960 --> 00:14:57,320 Like so and that should now remove the leading zeros because we're actually 258 00:14:57,320 --> 00:15:00,980 not printing anything until we get a non zero value the first time. 259 00:15:00,980 --> 00:15:02,740 We're setting printing to true. 260 00:15:02,740 --> 00:15:04,820 Of course it can be good practice printing 261 00:15:06,700 --> 00:15:09,430 equals false before we start the loop as well. 262 00:15:09,430 --> 00:15:12,370 We run that and we get to the number ten again. 263 00:15:14,330 --> 00:15:17,760 We're now left with one zero one zero which is again is the bond 264 00:15:17,760 --> 00:15:21,450 unit of decimal ten minus the zeros, the leading zeros. 265 00:15:21,450 --> 00:15:25,790 And you look at that and you think that works, and it mostly does the example I 266 00:15:26,900 --> 00:15:31,170 typed in it does but you should always test what are called boundary conditions. 267 00:15:31,170 --> 00:15:34,480 Now, these are boundaries that are at the extreme of allowing importance. 268 00:15:34,480 --> 00:15:36,360 So testing with the highest number allowed. 269 00:15:36,360 --> 00:15:38,740 65535, so we run it. 270 00:15:38,740 --> 00:15:39,340 65535. 271 00:15:39,340 --> 00:15:46,900 That works fine with all 1's remembering that that's the maximum number There. 272 00:15:46,900 --> 00:15:49,150 That we're allowed in this conversion. 273 00:15:49,150 --> 00:15:53,590 But, if we run it again and it's a zero, we get nothing. 274 00:15:53,590 --> 00:15:56,110 And of course zero is a valid binary number. 275 00:15:56,110 --> 00:15:57,080 So, how do we fix that? 276 00:15:57,080 --> 00:15:59,220 Well, the cure is to alter our tests so 277 00:15:59,220 --> 00:16:02,330 that we're actually setting printing to true as we can see on line 47. 278 00:16:02,330 --> 00:16:05,520 But we want to actually test that. 279 00:16:05,520 --> 00:16:07,070 Bit is not equal to zero. 280 00:16:07,070 --> 00:16:09,560 Or that we're processing the last power. 281 00:16:09,560 --> 00:16:13,880 In other words, processing the very last digit if you will on r in binary. 282 00:16:13,880 --> 00:16:17,960 So you can put all power is equal to 1. 283 00:16:17,960 --> 00:16:19,680 First you run that. 284 00:16:19,680 --> 00:16:24,690 Then we type 0, which you get a 0 chart which is correct cause the last power. 285 00:16:24,690 --> 00:16:29,210 Was calculated correctly and our condition was actually 286 00:16:29,210 --> 00:16:32,990 executed because the power was one and we hadn't had a zero up until then. 287 00:16:32,990 --> 00:16:36,120 The 65535 should still work as you can see on the screen there. 288 00:16:36,120 --> 00:16:39,810 The other you can do if you wanted to is you can play around with this 289 00:16:39,810 --> 00:16:43,740 looking at line The line where we use 15. 290 00:16:43,740 --> 00:16:47,370 So what we could do here is we could actually convert this to octal, 291 00:16:47,370 --> 00:16:47,870 our result. 292 00:16:47,870 --> 00:16:52,080 We could change the two here to an eight because two was for binary. 293 00:16:52,080 --> 00:16:55,980 We could actually change that to an eight to work in octal if we wanted to. 294 00:16:55,980 --> 00:16:57,820 And for efficiency, you should also reduce the range. 295 00:16:57,820 --> 00:17:01,790 Because the highest power of 8 we're now interested in is basically 262,144, 296 00:17:01,790 --> 00:17:04,560 which is greater than the highest number we're allowing for binary. 297 00:17:04,560 --> 00:17:07,810 So play around with that, as well. 298 00:17:07,810 --> 00:17:08,390 And you can do. 299 00:17:08,390 --> 00:17:10,890 Do something similar by converting it to octal. 300 00:17:10,890 --> 00:17:14,410 I'm gonna finish this video now but leave you with something to think about. 301 00:17:14,410 --> 00:17:16,510 So we shouldn't have actually written any code for this challenge. 302 00:17:16,510 --> 00:17:21,710 The specifications stated that the program should be coded for numbers up to 65,5- 303 00:17:21,710 --> 00:17:26,170 35, but with that said [INAUDIBLE] which would happen if a larger number is entered 304 00:17:26,170 --> 00:17:29,110 and there's also an assumption that the numbers would be positive. 305 00:17:29,110 --> 00:17:31,900 The problem here was the specification was inadequate. 306 00:17:31,900 --> 00:17:34,860 So, as programmers, we've got a duty of care to the people we're programming for 307 00:17:34,860 --> 00:17:38,530 and if we give it a specification that leaves such questions unanswered 308 00:17:38,530 --> 00:17:41,170 then we really need to go back to whoever produced the spec and 309 00:17:41,170 --> 00:17:44,350 seek clarification before producing any code. 310 00:17:44,350 --> 00:17:45,890 So that's it I am going to end the video there. 311 00:17:45,890 --> 00:17:47,210 I hope that's been helpful to you. 312 00:17:47,210 --> 00:17:49,250 We will see you now in the next section.