Number Systems Introduction - Decimal, Binary, Octal & Hexadecimal — Transcript

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1. 0:00in this video we're going to talk about
2. 0:02number
3. 0:03systems the first number system that you
4. 0:05need to be familiar with
5. 0:07is the decimal system
6. 0:10now when you hear the word decimal what
7. 0:12do you think of think of the prefix deci
8. 0:15what does that mean when i hear the word
9. 0:19deci
10. 0:20i think of one-tenth of a whole for
11. 0:23example
12. 0:24there's ten decimeters in one meter i
13. 0:27also think of the word decade
14. 0:30a decade corresponds to 10 years
15. 0:34and so deci is associated with 10 and in
16. 0:37fact
17. 0:38the decimal number system is
18. 0:42a base 10 system and so what this means
19. 0:45is that
20. 0:46there's 10 different numbers in the
21. 0:49decimal system
22. 0:510 1 2 3
23. 0:544 5 6 7
24. 0:588 and 9. so that's a total of 10 numbers
25. 1:03now this system is used for everyday
26. 1:06counting for example
27. 1:0712 or 36 or 468
28. 1:12we use the decimal system to represent
29. 1:14numbers
30. 1:15and it works pretty well now the next
31. 1:17system that you need to be familiar with
32. 1:19is the binary system so when you hear
33. 1:22the prefix buy
34. 1:24what do you think of bi means two
35. 1:28and so the binary system is a base two
36. 1:31system
37. 1:32it's very useful for computers or any
38. 1:35type of digital circuits
39. 1:36there's only two numbers here zero and
40. 1:39one
41. 1:40in a typical digital computer zero means
42. 1:43off
43. 1:45one means that the system is in the on
44. 1:47state
45. 1:49next we have the octosystem
46. 1:52and when you hear the word octo or octa
47. 1:55what do you think of
48. 1:57i think of an octagon an octagon is
49. 2:00basically a polygon
50. 2:02with eight sides so octa means
51. 2:06eight so the octal number system is
52. 2:09a base eight system so there's eight
53. 2:12numbers that we can use in the system
54. 2:14the first being zero and then one two
55. 2:17three
56. 2:18four five six seven so that's a total of
57. 2:22eight numbers including zero
58. 2:26next we have the hexadecimal system
59. 2:31now what is meant by the prefix hexa
60. 2:35hexa think of a hexagon
61. 2:38a hexagon has six sides and so hexa
62. 2:42means six we know decimal corresponds to
63. 2:46ten
64. 2:46and so six plus ten will give us sixteen
65. 2:49therefore the hexadecimal system
66. 2:51is a base 16 system
67. 2:55and so the numbers are 0 1 2
68. 2:583 4 5 6 7
69. 3:028 9 so we have all ten numbers in
70. 3:05the decimal system but we also have
71. 3:09six letters and so those letters are
72. 3:12a b c d
73. 3:15e and f now a corresponds to 10
74. 3:20in the decimal system b in the
75. 3:22hexadecimal system
76. 3:23corresponds to 11 in the decimal system
77. 3:26c is 12
78. 3:27d is 13 e is 14 f
79. 3:31is 15. so that's a total of 16 numbers
80. 3:34including zero
81. 3:36now let's talk about how we can convert
82. 3:39a decimal number
83. 3:40to a binary number and into an octal and
84. 3:43a hexadecimal number
85. 3:45using the technique called successive
86. 3:47division
87. 3:49so let's say we have the number 348
88. 3:52if you see a subscript 10 that means
89. 3:54it's in the base 10
90. 3:55system which means it's a decimal number
91. 3:58so the first thing you want to do is
92. 3:59take 348
93. 4:01and divide it by two
94. 4:04so if you type that in you'll get
95. 4:07exactly
96. 4:08174 so it's 174
97. 4:11remainder is zero next take 174
98. 4:15and then divide that by two so that's
99. 4:18exactly 87
100. 4:20so it's 87 remainder zero
101. 4:23next if we take 87 and divided by two
102. 4:28we're going to get 43.5
103. 4:31so it's 43 remainder one
104. 4:35but first let's write it like this
105. 4:39so this 43 gets transferred here
106. 4:42and then to get the remainder one you
107. 4:44multiply two by point five
108. 4:46and that will give you the remainder one
109. 4:51i'm going to write my answer like this
110. 4:53for now
111. 4:55now if we take 43 and divide that by two
112. 5:00that's going to be 21.5 which is 21
113. 5:04remainder one and then we need to take
114. 5:0621 divide that by two
115. 5:07so that's 10.5 which is
116. 5:1010 remainder 1 and then 10
117. 5:14divided by 2 is exactly 5 so 5 remainder
118. 5:170
119. 5:18and then 5 divided by 2 is 2.5
120. 5:21so 2 remainder one and then
121. 5:25two divided by two is exactly one so one
122. 5:28remainder is zero
123. 5:30and then one divided by
124. 5:34i'm running out of space here one
125. 5:35divided by two that's
126. 5:370.5 so 0 remainder
127. 5:401. what we have on top is the least
128. 5:43significant bit
129. 5:45and this here is the most significant
130. 5:48bit
131. 5:49now you can find your answer just by
132. 5:51looking at all of the remainder values
133. 5:55which is here
134. 5:58and so that's the binary number that's
135. 6:01equivalent
136. 6:02to 348 so you need to read it
137. 6:05from the bottom to the top so the answer
138. 6:08is
139. 6:081 0 1 0
140. 6:13and then 1 1 1
141. 6:170 0.
142. 6:20so that's how we can convert a decimal
143. 6:22number into
144. 6:23a binary number using successive
145. 6:26division
146. 6:29now let's convert this number into
147. 6:33an octal number in the base eight system
148. 6:37so if we look at the last example where
149. 6:40we converted 348 into a binary number
150. 6:43we were dividing it by two because
151. 6:45binary it's based on the base two system
152. 6:47by means two
153. 6:49the octal system is based on the base
154. 6:51eight system
155. 6:52so instead of dividing it by two and
156. 6:54collecting the remainders
157. 6:56we're going to divide it by eight this
158. 6:58time
159. 6:59so 3 48 divided by eight
160. 7:05that's going to be 43.5
161. 7:10so this is 43 remainder
162. 7:13now to find the remainder multiply 8
163. 7:16by 0.5 so 8 times 0.5
164. 7:20is 4 so it's 43 remainder 4.
165. 7:24next take 43 and divide it by 8. and
166. 7:30this will give you
167. 7:31five point three seven five
168. 7:34so it's five remainder and then multiply
169. 7:37the eight
170. 7:38by point three seven five eight times
171. 7:41point three seven five that will give
172. 7:43you
173. 7:43three next take the five
174. 7:46and divided by eight now five is less
175. 7:49than eight so we can say that eight
176. 7:51goes into five zero times with a
177. 7:54remainder of five
178. 7:55but if you do five divided by eight
179. 7:57you're going to get 0.625
180. 8:01and so the 0 gets transferred here
181. 8:04and then if you multiply 8 by 0.625 you
182. 8:07should get this number
183. 8:08the original number that you started
184. 8:10with which will go here
185. 8:13so this is the most significant digit
186. 8:16and above we have the least significant
187. 8:18digit so we're going to read it from the
188. 8:20bottom to the top
189. 8:22so 348 base 10
190. 8:26as a decimal number is equivalent to 5
191. 8:293 4 or 534 in the octal system
192. 8:34and so that's how you can convert a
193. 8:35decimal number into an octal number
194. 8:38using successive division
195. 8:42now let's talk about how to convert the
196. 8:44decimal number
197. 8:46into a hexadecimal number using
198. 8:49successive division
199. 8:52so let's use the same number 348.
200. 8:55let's convert it to a hexadecimal number
201. 8:58now the hexadecimal number is basically
202. 9:01a number in the base
203. 9:0216 system so this time instead of
204. 9:05dividing by
205. 9:062 or 8 we're going to divide by 16.
206. 9:11so if we take 348 and divided by 16
207. 9:15this will give us 21.75
208. 9:20and so that's 21 remainder
209. 9:23to find the remainder multiply 16 by
210. 9:260.75 so 16 times 0.75
211. 9:30that's 12. so it's 21 remainder 12.
212. 9:36now let's take 21 and then let's divide
213. 9:38that by 16.
214. 9:40so 21 divided by 16 is 1.3125
215. 9:47and so we have one remainder
216. 9:50now let's multiply 16 by 0.3125
217. 9:55and that's going to give us five so it's
218. 9:58a one remainder five
219. 10:00next take one divided by sixteen
220. 10:03now we know one doesn't go into 16 so 16
221. 10:06goes into one zero times
222. 10:08with a remainder of whatever you see
223. 10:10here in this case a remainder of one
224. 10:13and so we're going to read it this way
225. 10:15so we have
226. 10:16a 1 a 5 and a 12.
227. 10:21now 12 because it's larger than 9 we
228. 10:23need to convert it to a letter
229. 10:25so remember 10 corresponds to a
230. 10:2911 corresponds to b and 12 corresponds
231. 10:32to c
232. 10:33so it's 1 5 c so therefore
233. 10:38we could say this 348
234. 10:43in the base 10 system is 1 5c
235. 10:47in the base 16 system and so that's how
236. 10:50we can convert
237. 10:51a decimal number into a hexadecimal
238. 10:53number
239. 10:54using successive division