1
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Hey, guys, what's up?

2
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So in the last video, we learn how those two numbers are stored, how those are stored and how my floating

3
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point numbers are stored.

4
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So in this video, we will learn how negative numbers are stored.

5
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For example, I have four bytes of memory space and here's my data.

6
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I want to find what is the largest and what is the smallest number that I can store.

7
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I want to find the value of A and B.

8
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OK, so for simplification, let's say let's say I have four bids.

9
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That is half a bite.

10
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So I want to find the value of A and B for four bids.

11
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OK.

12
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So, OK, so what does the largest number that I can store.

13
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Obviously when, when, when and when that is plus seven.

14
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And what is the smallest number that I can store and for.

15
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Zero zero zero and zero net is zero.

16
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OK.

17
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So if I followed this presentation, the maximum value that I can store is plus seven and the minimum

18
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value that Igen stories zero.

19
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OK.

20
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But there's a very major problem with this approach, and the problem is we have never done.

21
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But also we have minus 10, we have minus eight.

22
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We have minus seven.

23
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We need negative number also.

24
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So how does two negative numbers.

25
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So let us talk about the first approach.

26
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OK, so the first upload sees what is the difference between then and minus 10?

27
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This is the only difference you will see and be right then and they will put a negative sign.

28
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OK.

29
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So what do we do if I if I have four kids?

30
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I will use my first word as a sign, but if it is when my number is negative.

31
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If it is zero, my number is positive and remaining, Tibbits will be used to find magnitude.

32
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Okay, so in this way, our problem will be resolved and we can and we will be able to represent negative

33
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numbers also.

34
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Okay, so let's see what is the largest and what is the smallest number.

35
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So for finding the largest number.

36
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I have four bids.

37
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First of all, I just number will be positive.

38
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So the first bid will be zero and the remaining three bid all will be won.

39
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To maximize the magnitude.

40
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So this is plus seven means positive and religious.

41
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My list number two can store.

42
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So I have four bids for a small listener.

43
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But what will I do?

44
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I will make my first bid when that is negative number and I will maximize the manged.

45
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That is when, when and when.

46
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So this is seven.

47
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My number is negative.

48
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So this is a business minus seven.

49
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Now, what is our range?

50
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Our ranges from minus seven to plus seven.

51
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So obviously this approach is much better than our previous approach.

52
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Why?

53
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Because in this approach, we are able to store negative numbers also.

54
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But there's a problem with this approach also.

55
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And what is the problem?

56
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OK, so tell me, what does this number.

57
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So zero means?

58
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My number is positive.

59
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And this represent zero.

60
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So my number is plus zero.

61
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Now tell me, what is this number?

62
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So one means my number is negative.

63
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And this represent magnitude.

64
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So my number is minus zero.

65
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So you can see here there are two representation of zero zero and minus zero.

66
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OK.

67
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So there is ambiguity in the representation of zero.

68
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And we will resolve it.

69
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So how we can resolve it.

70
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What we will do.

71
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OK, so how we can resolve it.

72
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What we will do.

73
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We will do some minor changes for positive, no representation.

74
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We will follow the above approach that is signed.

75
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But the first word will be used to assign it.

76
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And the remaining bits will be used as magnitude.

77
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So positive.

78
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No representation.

79
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I will use the above approach for negative numbers.

80
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We have something called to complement.

81
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Those compliment form.

82
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OK.

83
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So negative numbers are represented in those compliment form.

84
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Now, what is to this compliment?

85
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So it does compliment is actually once compliment.

86
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Plus, when and how to find device complement, which is very simple, you just flip all the bits,

87
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flip all the bits of a tiny number, and what you will have is called Wendt's complement.

88
00:05:32,530 --> 00:05:34,140
OK, so let's see some example.

89
00:05:36,390 --> 00:05:38,670
For example, I want to store minus two.

90
00:05:39,900 --> 00:05:40,770
So what do we do?

91
00:05:40,890 --> 00:05:42,030
First of all, we'll be right.

92
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Plus two.

93
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Plus two is zero.

94
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First bit positive and then magnitude, which is zero, one and zero.

95
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So this is blessed to now find one's complement, which is flip all the bits.

96
00:05:59,610 --> 00:06:08,910
So when one is zero and one NARVO finding to complement what you will do, you will add a plus one.

97
00:06:09,180 --> 00:06:11,190
So here you will do plus one.

98
00:06:12,390 --> 00:06:13,950
So my answer will be one.

99
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Plus one.

100
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OK, so before moving forward, let's see one more thing.

101
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What is Zeo Clezio in binary?

102
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Zero.

103
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What is a zero plus one in binary?

104
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One.

105
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What is one plus zero in binary one.

106
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So up to this, my binary and decimal both housein but one plus one in binary is equals to.

107
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This is the most important thing that you have to learn.

108
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That one plus one in binary is ten.

109
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Again in decimal one plus one is true, but in binary one plus one is ten.

110
00:06:59,970 --> 00:07:03,480
OK, so let's see some example of those complement.

111
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For example, you want to store minus two.

112
00:07:06,870 --> 00:07:07,770
So what you will do.

113
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First of all, you will write plus two.

114
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So zero.

115
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And then I am to present magnitude, which is zero one and zero.

116
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So this is plus two.

117
00:07:19,030 --> 00:07:22,730
Now you will find vice complement and whatever else compliment.

118
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Just flip all the bits.

119
00:07:25,180 --> 00:07:29,260
So when one zero and one.

120
00:07:29,410 --> 00:07:30,730
So this is W complement.

121
00:07:31,700 --> 00:07:35,540
Now for finding booze, complement what they will do, you will add one.

122
00:07:38,320 --> 00:07:46,700
So plus one one plus one is then when Gary, when blessed, always one.

123
00:07:47,190 --> 00:07:47,820
Then one.

124
00:07:47,940 --> 00:07:48,570
And then one.

125
00:07:49,230 --> 00:07:52,700
So this number represent minus two.

126
00:07:54,380 --> 00:07:57,040
OK, so this number represent minus two.

127
00:07:57,400 --> 00:07:57,570
OK.

128
00:07:57,710 --> 00:07:58,450
Let's do that.

129
00:07:58,450 --> 00:08:00,250
He was given.

130
00:08:02,140 --> 00:08:04,410
When, when, when and zero.

131
00:08:04,810 --> 00:08:08,770
So you have to find what this number is present in decimal.

132
00:08:10,030 --> 00:08:10,240
OK.

133
00:08:10,510 --> 00:08:11,410
So how we will do.

134
00:08:14,320 --> 00:08:15,100
So we will check.

135
00:08:16,060 --> 00:08:17,350
First word is negative.

136
00:08:19,450 --> 00:08:20,650
First word is negative.

137
00:08:20,710 --> 00:08:22,450
So my number is going to be negative.

138
00:08:23,100 --> 00:08:25,750
And for finding magnitude, what do will do?

139
00:08:26,080 --> 00:08:28,390
You will find two complement of this number.

140
00:08:29,560 --> 00:08:30,420
So it is a toothcomb.

141
00:08:30,550 --> 00:08:32,710
Does this number find a nice compliment?

142
00:08:32,890 --> 00:08:35,000
Zero zero zero one and one.

143
00:08:36,040 --> 00:08:37,060
So one plus one is.

144
00:08:38,920 --> 00:08:40,320
When Gary here.

145
00:08:40,330 --> 00:08:41,770
One zero zero.

146
00:08:42,340 --> 00:08:43,420
So what is the magnitude?

147
00:08:43,720 --> 00:08:45,090
Magnitude is two.

148
00:08:45,400 --> 00:08:46,900
And the number is negative.

149
00:08:47,110 --> 00:08:48,660
So this number is minus two.

150
00:08:49,840 --> 00:08:53,650
Okay, so if it was zero one one zero.

151
00:08:53,960 --> 00:08:54,730
So zero means.

152
00:08:54,790 --> 00:08:58,030
This number is Piloto then for finding magnitude.

153
00:08:58,120 --> 00:09:00,070
You will not calculate to complement.

154
00:09:00,740 --> 00:09:06,220
I calculated to compliment here because the number was negative and negative numbers are stored in those

155
00:09:06,220 --> 00:09:07,000
compliment form.

156
00:09:07,330 --> 00:09:10,560
That's why for finding magnitude I calculated boose complement.

157
00:09:11,020 --> 00:09:13,040
But says the number is positive.

158
00:09:14,980 --> 00:09:17,920
This Tribbett will represent magnitude.

159
00:09:18,820 --> 00:09:19,030
Okay.

160
00:09:19,510 --> 00:09:23,920
So this represent magnitude and it is four plus two six.

161
00:09:24,490 --> 00:09:26,380
So this number is plus six.

162
00:09:26,560 --> 00:09:28,270
And this number is minus two.

163
00:09:29,800 --> 00:09:30,070
Okay.

164
00:09:30,340 --> 00:09:33,940
So how we can prove that this number is minus two.

165
00:09:34,570 --> 00:09:35,170
So let's see.

166
00:09:36,520 --> 00:09:38,560
Okay, so let's do some vectors.

167
00:09:40,930 --> 00:09:41,200
Okay.

168
00:09:41,500 --> 00:09:45,370
Suppose you want to find what is five minus five.

169
00:09:45,910 --> 00:09:46,720
So what do we do.

170
00:09:47,320 --> 00:09:49,990
Five plus two is complement.

171
00:09:53,850 --> 00:09:58,430
Of faith, actually, there is nothing called subtract.

172
00:09:59,260 --> 00:10:02,190
There is nothing called septet logic circuit in computer system.

173
00:10:02,490 --> 00:10:09,300
We always have ideologic circuit because at our function at the logic circuit, then can do the work

174
00:10:09,320 --> 00:10:14,490
over subjective logic circuit and hence our hardway we reduce so will reduce the cost.

175
00:10:15,500 --> 00:10:17,060
So what is the five?

176
00:10:17,150 --> 00:10:24,380
Five is first spread will be zero and it will hurt the remaining three birds will represent magnitude

177
00:10:24,470 --> 00:10:25,330
one zero one.

178
00:10:25,700 --> 00:10:26,730
So this is plus five.

179
00:10:27,640 --> 00:10:29,570
Now we're finding does compliment of five.

180
00:10:30,050 --> 00:10:30,650
What will I do?

181
00:10:30,740 --> 00:10:32,510
I will, first of all, write five.

182
00:10:33,140 --> 00:10:36,880
Then find ways complement, which is one two two one zero.

183
00:10:37,370 --> 00:10:39,200
Then I will find to complement.

184
00:10:39,320 --> 00:10:42,680
Which is add one to the last position.

185
00:10:43,760 --> 00:10:46,610
One one zero and one.

186
00:10:47,450 --> 00:10:50,360
So this number is minus five.

187
00:10:50,780 --> 00:10:51,620
Now we will add.

188
00:10:51,980 --> 00:10:52,220
OK.

189
00:10:52,310 --> 00:10:55,610
So zero one zero one one zero one and one.

190
00:10:57,840 --> 00:11:07,370
So one plus one is then when Kerry one plus one is then one carry one plus one is then when ghetty one

191
00:11:07,370 --> 00:11:10,850
plus one is then when Gary and vividly discarded.

192
00:11:11,070 --> 00:11:14,810
OK, so we will discard it.

193
00:11:16,280 --> 00:11:17,680
So this is zero.

194
00:11:19,000 --> 00:11:19,190
OK.

195
00:11:19,640 --> 00:11:22,790
So five minus five should be zero and my for this coming out Billy.

196
00:11:23,330 --> 00:11:23,750
Zero.

197
00:11:25,510 --> 00:11:30,510
Let's see one more example, suppose you want to calculate.

198
00:11:31,210 --> 00:11:32,440
Seven minus seven.

199
00:11:32,810 --> 00:11:33,670
And there should be zero.

200
00:11:34,030 --> 00:11:36,340
So seven minus seven is same as seven.

201
00:11:36,340 --> 00:11:39,310
Plus two is complement of seven.

202
00:11:41,530 --> 00:11:45,820
So four representing seven, four squared will be zero.

203
00:11:45,850 --> 00:11:50,140
And that meaning tribute will be one for to complement of seven.

204
00:11:50,200 --> 00:11:50,700
Will Villedieu.

205
00:11:51,240 --> 00:11:52,240
I will first of all.

206
00:11:52,300 --> 00:11:58,450
Right seven find a complement one zero zero zero then those complement add one.

207
00:11:59,260 --> 00:12:00,520
So one zero zero one.

208
00:12:00,970 --> 00:12:02,740
So this is minus seven.

209
00:12:03,310 --> 00:12:07,060
Now add plus seven with minus seven.

210
00:12:07,090 --> 00:12:08,310
So one plus one is ten.

211
00:12:08,470 --> 00:12:11,320
When Gary went plus one new spin when gay one.

212
00:12:11,320 --> 00:12:11,690
Plus one.

213
00:12:11,920 --> 00:12:13,010
Then when Gary.

214
00:12:13,030 --> 00:12:13,990
When plus minus 10.

215
00:12:14,380 --> 00:12:16,060
When Gary and we were discarded.

216
00:12:18,700 --> 00:12:20,100
So this is my answer.

217
00:12:20,110 --> 00:12:21,160
That is zero.

218
00:12:22,000 --> 00:12:27,040
So I hope by this time you'll know know how to find those complement.

219
00:12:28,180 --> 00:12:29,230
One last example.

220
00:12:29,800 --> 00:12:39,720
Suppose you are given this number one zero zero one and the second number is zero zero zero one.

221
00:12:40,690 --> 00:12:42,770
So this number means zero means.

222
00:12:42,790 --> 00:12:43,750
My number is positive.

223
00:12:44,180 --> 00:12:45,330
Has done the most positive.

224
00:12:46,390 --> 00:12:50,410
Remaining list will represent the magnitude that is Mangere is one.

225
00:12:50,620 --> 00:12:52,090
So number is plus one.

226
00:12:53,100 --> 00:12:56,520
Now, in this case, first bid is when it meets.

227
00:12:56,530 --> 00:12:57,460
My number is negative.

228
00:12:57,910 --> 00:13:02,110
So for finding magnitude, I will find it to complement.

229
00:13:03,580 --> 00:13:04,570
To complement.

230
00:13:05,800 --> 00:13:07,410
So what that do is complement of this number.

231
00:13:08,250 --> 00:13:11,080
One zero zero one find one's complement.

232
00:13:11,730 --> 00:13:14,250
So one's compliment is zero one one zero.

233
00:13:14,880 --> 00:13:17,880
Now for finding does compliment add one plus one.

234
00:13:18,550 --> 00:13:20,160
It is zero one one one.

235
00:13:20,580 --> 00:13:23,370
So what is the magnitude man this coming out to be?

236
00:13:23,730 --> 00:13:24,210
Seven.

237
00:13:24,660 --> 00:13:26,310
So the number is negative.

238
00:13:27,720 --> 00:13:29,100
And the main dude is seven.

239
00:13:29,130 --> 00:13:31,590
So this number represent minus seven.

240
00:13:32,560 --> 00:13:35,220
Okay, so now let's come back to our problem.

241
00:13:35,370 --> 00:13:40,680
Our problem was zero was having two representations, zero and plus zero.

242
00:13:45,300 --> 00:13:46,140
OK, so let's see.

243
00:13:46,890 --> 00:13:48,510
Zero means my number is positive.

244
00:13:48,990 --> 00:13:50,520
And this represent zero.

245
00:13:50,580 --> 00:13:52,230
That means my number is below zero.

246
00:13:56,100 --> 00:14:01,020
Now, in our previous approach, this by any number was representing minus zero.

247
00:14:01,290 --> 00:14:03,610
Now let's see what this number will represent.

248
00:14:03,750 --> 00:14:04,890
And to compliment from.

249
00:14:06,040 --> 00:14:08,190
So one means my number is negative.

250
00:14:08,590 --> 00:14:10,200
And hence numbers negative.

251
00:14:10,420 --> 00:14:14,860
I will calculate my man, do my calculating lose complement.

252
00:14:17,220 --> 00:14:22,560
What is there to compliment of this number whose compliment is, first of all, one's compliment, which

253
00:14:22,560 --> 00:14:24,950
is zero one when one?

254
00:14:25,620 --> 00:14:33,600
Now, for finding those compliment, we will add plus one plus one one plus on this 10, one getti one

255
00:14:33,600 --> 00:14:41,330
plus one is then when ghetty one plus one is then one ghetty when president is zero sorry one.

256
00:14:42,510 --> 00:14:44,220
So this is my magnitude.

257
00:14:44,310 --> 00:14:45,420
That is it.

258
00:14:46,410 --> 00:14:49,920
Okay, so that number is negative and the magnitude is eight.

259
00:14:51,120 --> 00:14:54,840
So this number is minus eight.

260
00:14:56,370 --> 00:14:59,060
OK, so this number is minus eight.

261
00:14:59,510 --> 00:15:03,140
Now, something very interesting happened here in our previous approach.

262
00:15:03,650 --> 00:15:09,080
My range was minus seven, two plus seven.

263
00:15:11,720 --> 00:15:15,290
But falling the does compliment form does compliment approach.

264
00:15:15,650 --> 00:15:21,800
My range has been increased from minus eight to plus seven.

265
00:15:21,950 --> 00:15:22,910
And why this happens?

266
00:15:23,270 --> 00:15:28,670
Because in this case, zero was having to do presentations plus zero and minus zero.

267
00:15:29,090 --> 00:15:34,280
And in this case, minus zero is representing minus eight.

268
00:15:34,700 --> 00:15:37,040
So that's why there is an increase in the range.

269
00:15:38,030 --> 00:15:40,880
OK, so my final ranges, minus eight.

270
00:15:41,450 --> 00:15:42,590
Two plus seven.

271
00:15:43,070 --> 00:15:44,910
It is four forwards.

272
00:15:46,610 --> 00:15:47,660
That is we can right.

273
00:15:48,140 --> 00:15:49,970
Minus two to the power four.

274
00:15:50,030 --> 00:15:50,810
Minus one.

275
00:15:56,300 --> 00:15:59,860
Twittered about four, minus one and here minus one.

276
00:16:00,460 --> 00:16:04,780
So this is so Forbert now we can generalize it for Edwards.

277
00:16:05,620 --> 00:16:16,150
So if I'm having Edwards, my range will be minus two to the power and minus one to.

278
00:16:18,270 --> 00:16:20,540
Due to the power and minus one minus.

279
00:16:21,850 --> 00:16:23,310
OK, so let's see.

280
00:16:23,980 --> 00:16:24,820
Four characters.

281
00:16:24,910 --> 00:16:29,220
I have one bite that is Edwards.

282
00:16:30,130 --> 00:16:31,600
So it is a range of characters.

283
00:16:31,840 --> 00:16:39,640
The range of this will be minus two to the power and seven to go to about seven.

284
00:16:39,970 --> 00:16:40,480
Minus one.

285
00:16:40,480 --> 00:16:41,570
That is minus one.

286
00:16:41,590 --> 00:16:44,090
Twenty eight to one.

287
00:16:44,110 --> 00:16:45,430
Twenty seven.

288
00:16:46,690 --> 00:16:50,310
And we all know nine to five represent a night.

289
00:16:50,440 --> 00:16:52,530
Sorry, 97 represent Smally.

290
00:16:53,440 --> 00:16:54,760
Ninety eight represent.

291
00:16:54,850 --> 00:16:56,690
Be 65 percent.

292
00:16:56,920 --> 00:16:57,580
Capitally.

293
00:16:57,670 --> 00:16:58,330
And so on.

294
00:16:59,290 --> 00:16:59,670
And voting.

295
00:17:00,430 --> 00:17:02,920
I am having to do two bits.

296
00:17:04,870 --> 00:17:05,700
So for integers.

297
00:17:05,800 --> 00:17:07,170
I have to do two bits.

298
00:17:07,660 --> 00:17:15,280
That is my range will be minus two to the power 31 to two to the power 31.

299
00:17:15,550 --> 00:17:16,510
Minus one.

300
00:17:17,200 --> 00:17:17,440
Okay.

301
00:17:17,710 --> 00:17:19,330
So this is the range of integers.

302
00:17:21,590 --> 00:17:27,650
OK, so this value is close to 10 to the Bauer nine and this value is close to the end of the ballot.

303
00:17:28,040 --> 00:17:29,450
Nine minus 10 to the Bauer nine.

304
00:17:30,080 --> 00:17:38,150
So, in short, you can remember that if I am having nine digits in a number, if there are nine digits

305
00:17:38,150 --> 00:17:42,350
in number, that number can be stored in and the other type.

306
00:17:43,070 --> 00:17:54,770
And similarly, if we have long, longer to type in loan order type, I have 64 Edwards because it is

307
00:17:54,770 --> 00:17:55,600
of a debate.

308
00:17:55,970 --> 00:18:02,750
So my range will be minus troupers, about six to three to the power, 63 minus one.

309
00:18:03,440 --> 00:18:04,940
So this is close to 10.

310
00:18:04,940 --> 00:18:06,020
To the power 18.

311
00:18:06,860 --> 00:18:09,140
And this is close to 10.

312
00:18:09,140 --> 00:18:10,640
To the power minus 10.

313
00:18:10,640 --> 00:18:11,650
To the power 18.

314
00:18:12,410 --> 00:18:24,200
So that means if I am having 18 digits against door, that number in long, long is that number of digits

315
00:18:24,200 --> 00:18:25,730
are less than Oracle's 218.

316
00:18:26,180 --> 00:18:33,410
But if the number of digits are less than Oracle is to nine, I can store it in and I can also store

317
00:18:33,410 --> 00:18:34,860
it in long, long time.

318
00:18:35,030 --> 00:18:37,040
But we can also store in integers.

319
00:18:38,150 --> 00:18:46,040
So if there is a number having more than 18 digits, it is a number having more than 18 digits.

320
00:18:46,400 --> 00:18:47,930
I can not store it.

321
00:18:48,370 --> 00:18:48,660
Okay.

322
00:18:49,250 --> 00:18:50,540
It cannot store it.

323
00:18:51,110 --> 00:18:54,470
Longlong cannot store it.

324
00:18:55,290 --> 00:18:55,580
Okay.

325
00:18:57,910 --> 00:18:58,750
OK, guys.

326
00:18:58,840 --> 00:19:00,400
So this is it for this video.

327
00:19:00,640 --> 00:19:01,510
Thanks for watching.
