WEBVTT 00:00.400 --> 00:01.240 Hello, everyone. 00:01.880 --> 00:02.640 I'm typhoon. 00:02.920 --> 00:10.600 Welcome to today's comprehensive lecture on binary subtraction and handling signed integers using two's 00:10.640 --> 00:11.440 complement. 00:12.080 --> 00:17.800 We will explore important concepts clearly and interactively to help you deeply understand how computers 00:17.800 --> 00:20.800 perform arithmetic with signed numbers. 00:21.520 --> 00:27.160 In binary arithmetic, numbers can be positive or negative. 00:27.840 --> 00:34.480 To represent this in binary, we typically use one bit, known as the sign bit. 00:35.160 --> 00:38.760 This is the sign bit in assigned integers. 00:38.760 --> 00:41.560 In unsigned integers, we don't have a sign bit. 00:41.600 --> 00:46.440 Since we don't have a sign bit, we have more values to store. 00:47.120 --> 00:55.000 But the drawback is in unsigned integers we don't have a negative numbers, so the sign bit indicates 00:55.000 --> 00:58.440 whether a number is positive or negative. 00:59.080 --> 01:05.740 Initially, you might consider simply just that this zero. 01:06.260 --> 01:11.260 If you have zero in assigned integers as a first bit, it is. 01:11.300 --> 01:11.660 What? 01:11.700 --> 01:12.740 Positive, right? 01:13.140 --> 01:16.900 But here if we have one, it means it is negative. 01:17.580 --> 01:24.820 However, this straightforward method known as sign magnitude leads to problems when adding numbers. 01:25.420 --> 01:28.340 Now let's look at a simple example here. 01:28.740 --> 01:31.980 So we have what zero one. 01:32.020 --> 01:34.780 Or let's use another color for this. 01:35.540 --> 01:42.060 We have 0010 which is what. 01:42.740 --> 01:43.580 Positive two. 01:44.140 --> 01:48.460 And 1010. 01:48.500 --> 01:49.300 Which is what. 01:49.700 --> 01:50.580 Negative two. 01:51.100 --> 01:55.540 And if you calculate that what we will get one one. 01:56.260 --> 02:03.240 The result is 1100 which represents what Minus four instead of two. 02:03.480 --> 02:05.400 But the real result should be. 02:05.440 --> 02:05.760 What? 02:05.800 --> 02:06.200 Two. 02:06.840 --> 02:07.280 Zero. 02:07.760 --> 02:12.320 Now, clearly a different method is needed here to overcome this problem. 02:13.080 --> 02:17.400 Most computers use two complement notation. 02:17.440 --> 02:22.480 Before we dive deeper, let's clearly understand complement concepts in mathematics. 02:22.720 --> 02:30.360 Now we have the complement of number a number you add to another to reach a specific base or whole. 02:31.120 --> 02:34.840 Example is the complement of 37. 02:34.880 --> 02:39.840 In base ten which is decimal with two digits are 63. 02:39.960 --> 02:47.640 Because what 37 plus 63 is 100, right? 02:48.280 --> 02:51.920 This is complement and the two's complement in binary. 02:52.600 --> 02:59.200 Now for binary numbers two's complement is simple way to represent negative numbers allowing easy addition 02:59.200 --> 03:00.760 and subtraction operations. 03:00.760 --> 03:02.460 Us now here. 03:02.860 --> 03:08.140 Let's look at how two's complement notation works practically in binary arithmetic. 03:08.820 --> 03:13.460 Here you see plus one is 0000010. 03:13.660 --> 03:19.180 And minus one is 1111110. 03:19.300 --> 03:24.700 So it works like in reverse basically. 03:25.100 --> 03:34.220 So key observations about two's complement is the first bit is often called the sign bit with what zero 03:34.220 --> 03:36.820 for positive and one for negative. 03:37.500 --> 03:43.620 This notation allows arithmetic operations without special instructions and the range from a four bit 03:43.660 --> 03:45.660 integer integer. 03:45.820 --> 03:48.740 So what we have here is four bits, right? 03:49.460 --> 03:57.340 The range for the four bit integer is what is from minus eight to plus seven. 03:58.060 --> 04:04.350 In the unsigned it can from 0 to 16 or 15 or 16, right? 04:05.030 --> 04:07.750 That's how it basically works. 04:08.470 --> 04:09.910 You get negative numbers. 04:10.110 --> 04:15.390 But the drawback is you will get twice less. 04:16.630 --> 04:23.750 Now let's revisit our previous example on adding plus two and minus two. 04:24.550 --> 04:26.270 This time using two's complement. 04:26.550 --> 04:30.550 So we will use again 0010. 04:30.550 --> 04:36.950 And the two is remember 11101110. 04:37.750 --> 04:42.550 And what we will get here is 0000. 04:42.990 --> 04:46.230 The result is zero correctly represents zero. 04:47.070 --> 04:49.830 Demonstrating the advantage of two's complement notation. 04:49.990 --> 04:56.910 Clearly here you can see zero is always 000 doesn't matter in an inside or outside right. 04:57.430 --> 05:03.530 To ensure you understand these concepts well here's a quick exercise using four bits four bit two's 05:03.530 --> 05:09.170 complement at minus three and plus three for the binary result. 05:09.170 --> 05:13.490 Clearly and explain yourself briefly on your own notepad. 05:13.890 --> 05:14.570 Pause the video. 05:14.570 --> 05:23.810 Now try to exercise yourself and resume the solution to see the solution here. 05:24.570 --> 05:35.130 The solution is but 1101 and 1100. 05:35.890 --> 05:44.850 This is minus three plus 311 goes as zero again 000. 05:45.170 --> 05:52.010 The binary result correctly represents zero, confirming our understanding of two's complement addition. 05:52.010 --> 05:53.570 So use complement. 05:54.170 --> 06:00.490 Now two's complement is extensively used in modern computing for arithmetic operations due to its efficiency. 06:00.530 --> 06:06.550 Now this simplicity in arithmetic circuits make it the standard across nearly all computing devices, 06:06.550 --> 06:08.830 from smartphones to supercomputers. 06:09.070 --> 06:15.710 Understanding these two's complement helps you grasp more complex computing principles clearly. 06:15.990 --> 06:22.950 And in today's lecture, we have covered why simple sine magnitude methods aren't practical for arithmetic. 06:23.590 --> 06:30.550 You see, when we try to use the minus one plus two, we got the wrong result here, right? 06:31.510 --> 06:35.950 And we also learned the importance and utility of two's complement notation. 06:36.230 --> 06:42.910 We also learned the practical examples and interactive exercises for adding and subtracting sine integers 06:42.910 --> 06:44.190 using two's complement. 06:44.790 --> 06:50.990 Now by mastering these concepts, you will well be prepared for advanced topics in computer organizations 06:51.390 --> 06:54.150 and computing or low level computing. 06:54.830 --> 06:56.630 Thanks for joining today's lecture. 06:56.630 --> 07:02.710 Feel free to ask any questions and I look forward to seeing you in our next lecture.