5 Fun Facts about Octal and Decimal Numbers:
- The word “octal” comes from the Latin word “octo,” which means “eight.” This reflects the fact that octal numbers are based on a base-8 numbering system, with each digit representing a value from 0 to 7.
- In octal notation, the digits 0-7 are used to represent values, while in decimal notation, the digits 0-9 are used. This means that the largest single-digit number in octal is 7, while in decimal it is 9.
- Octal numbers are often used in computer programming and other technical fields because they are a compact and easily readable way to represent binary data. Each octal digit represents 3 bits of binary data, so a 16-bit binary number can be represented using 5 octal digits.
- In mathematics, octal numbers are sometimes used to represent very large numbers that would be difficult to read and work with using traditional decimal notation. For example, the number 7777777 in octal represents the much larger number 2097151 in decimal.
- In some programming languages, octal numbers are indicated by a leading zero, such as 0777. This helps to distinguish them from decimal numbers, which do not have a leading zero.
5 Benefits about Octal and Decimal Numbers:
- Compact representation: Hexadecimals and decimals allow large numbers to be represented using fewer digits than would be required in other numbering systems. This can be especially useful when working with large amounts of data or when space is limited.
- Easier to read: Both hexadecimals and decimals use a combination of digits, which can make them easier to read and distinguish from one another than other numbering systems.
- More user-friendly: Hexadecimals and decimals are often used in computer programming and other technical fields because they are easier for humans to read and understand than binary or other low-level representations.
- More efficient: Both hexadecimals and decimals can be more efficient to use in certain contexts, such as when working with large amounts of data that need to be stored or transmitted.
- Widely used: Both hexadecimals and decimals are used in a variety of fields, including computer programming, web development, and data storage, which means that they are useful skills to have in many different professional contexts.
5 Funny Jokes about Numbers:
- “Why was the math book sad? Because it had too many problems.”
- “Why was 6 afraid of 7? Because 7 8 9.”
- “I tried to calculate how many sheep there were in Wales, but I kept getting Wales is not sheep.”
- “Why did the tomato turn red? Because it saw the salad dressing!”
- “Why was the number 4 unhappy? Because it was two squared and didn’t want to be squared away.”
Frequently Asked Questions
What is an Octal Number?
An octal number is a number written using the base-8 numbering system. In this system, the digits 0-7 are used to represent values, with each digit representing a power of 8.
How do you convert 0.25 to octal?
The octal equivalent of the decimal number 0.25 is 0.02.
What is the octal equivalent of decimal number 8?
The octal equivalent of the decimal number 8 is 10.
Decimal To Octal
Decimal System
The decimal numeral framework is the most normally utilized and the standard framework in day by day life. It utilizes the number 10 as its base (radix). In this way, it has 10 images: The numbers from 0 to 9; in particular 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
As one of the most established known numeral frameworks, the decimal numeral framework has been utilized by numerous antiquated civilizations. The trouble of addressing extremely enormous numbers in the decimal framework was overwhelmed by the Hindu–Arabic numeral framework. The Hindu-Arabic numeral framework offers positions to the digits in a number and this technique works by utilizing forces of the base 10; digits are raised to the nth force, as per their position.
For example, take the number 2345.67 in the decimal framework:
The digit 5 is in the situation of ones (100, which approaches 1),
4 is in the situation of tens (101)
3 is in the situation of hundreds (102)
2 is in the situation of thousands (103)
In the interim, the digit 6 after the decimal point is in the tenths (1/10, which is 10-1) and 7 is in the hundredths (1/100, which is 10-2) position
In this way, the number 2345.67 can likewise be addressed as follows: (2 * 103) + (3 * 102) + (4 * 101) + (5 * 100) + (6 * 10-1) + (7 * 10-2)
Octal Number System:
The octal numeral framework is the base 8 number framework, and utilizes the digits from 0 to 7. Octal numerals can be produced using binary numerals by gathering continuous binary digits into gatherings of three (beginning from the right).
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Converting Decimal To octal
To change decimal over to octal, we need to find out about both the number framework first. Here we will change a decimal number over to an identical octal number. It is same as changing any decimal number over to parallel or decimal to hexadecimal.
In decimal to double, we partition the number by 2, in decimal to hexadecimal we partition the number by 16. In the event of decimal to octal, we partition the number by 8 and compose the remnants in the converse request to get the same octal number.
Convert Decimal to Octal with Steps Follow the means offered underneath to get familiar with the decimal to octal change:
1. Compose the given decimal number
2. In the event that the given decimal number is under 8 the octal number is something very similar.
3. In the event that the decimal number is more prominent than 7, partition the number by 8.
4. Note the rest of, get after division
5. Do stage 3 and 4 with the remainder till it is under 8
6. Presently, compose the leftovers in invert request (base to top)
7. The resultant is the same octal number to the given decimal number.
Changing over with Remainders (For whole number part)
This is a direct strategy which include separating the number to be changed over. Let decimal number is N then, at that point partition this number from 8 since base of octal number framework is 8. Note down the worth of leftover portion, which will be − 0, 1, 2, 3, 4, 5, 6, or 7. Again partition staying decimal number till it became 0 and note each rest of each progression. Then, at that point compose leftovers from base to up (or in turn around request), which will be comparable octal number of given decimal number. This is method for changing over a number decimal number, calculation is given underneath.
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- Accept decimal number as profit.
- Separation this number by (8 is base of octal so divisor here).
- Store the rest of a cluster (it will be: 0, 1, 2, 3, 4, 5, 6 or 7 on account of divisor 8).
- Rehash the over two stages until the number is more noteworthy than nothing.
- Print the cluster backward request (which will be identical octal number of given decimal number).
Note that profit (here given decimal number) is the number being isolated, the divisor (here base of octal, i.e., 8) in the number by which the profit is separated, and remainder (staying partitioned decimal number) is the consequence of the division.
Changing over with Remainders (For fragmentary part)
Let decimal partial part is M then increase this number from 8 since base of octal number framework is 8. Note down the worth of whole number part, which will be − 0, 1, 2, 3, 4, 5, 6, and 7. Again increase staying decimal partial number till it became 0 and note each whole number piece of consequence of each progression. Then, at that point compose noted aftereffects of number part, which will be comparable portion octal number of given decimal number. This is system for changing over a fragmentary decimal number, calculation is given underneath.
- Accept decimal number as multiplicand.
- Various this number by (8 is base of octal so multiplier here).
- Store the worth of whole number piece of result in a cluster (it will be: 0, 1, 2, 3, 4, 5, 6, and 7 in light of multiplier 8).
- Rehash the over two stages until the number became zero.
- Print the cluster (which will be comparable fragmentary octal number of given decimal partial number).
Note that a multiplicand (here decimal fragmentary number) is that to be duplicated by multiplier (here base of octal, i.e., 8)
Decimal to Octal Conversion Chart Table
Octal | |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
8 | 10 |
9 | 11 |
10 | 12 |
11 | 13 |
12 | 14 |
13 | 15 |
14 | 16 |
15 | 17 |
16 | 20 |
17 | 21 |
18 | 22 |
19 | 23 |
20 | 24 |
21 | 25 |
22 | 26 |
23 | 27 |
24 | 30 |
25 | 31 |
26 | 32 |
27 | 33 |
28 | 34 |
29 | 35 |
30 | 36 |
31 | 37 |
32 | 40 |
33 | 41 |
34 | 42 |
35 | 43 |
36 | 44 |
37 | 45 |
38 | 46 |
39 | 47 |
40 | 50 |
41 | 51 |
42 | 52 |
43 | 53 |
44 | 54 |
45 | 55 |
46 | 56 |
47 | 57 |
48 | 60 |
49 | 61 |
50 | 62 |
51 | 63 |
52 | 64 |
53 | 65 |
54 | 66 |
55 | 67 |
56 | 70 |
57 | 71 |
58 | 72 |
59 | 73 |
60 | 74 |
61 | 75 |
62 | 76 |
63 | 77 |
64 | 100 |
Decimal | Octal |
65 | 101 |
66 | 102 |
67 | 103 |
68 | 104 |
69 | 105 |
70 | 106 |
71 | 107 |
72 | 110 |
73 | 111 |
74 | 112 |
75 | 113 |
76 | 114 |
77 | 115 |
78 | 116 |
79 | 117 |
80 | 120 |
81 | 121 |
82 | 122 |
83 | 123 |
84 | 124 |
85 | 125 |
86 | 126 |
87 | 127 |
88 | 130 |
89 | 131 |
90 | 132 |
91 | 133 |
92 | 134 |
93 | 135 |
94 | 136 |
95 | 137 |
96 | 140 |
97 | 141 |
98 | 142 |
99 | 143 |
100 | 144 |
101 | 145 |
102 | 146 |
103 | 147 |
104 | 150 |
105 | 151 |
106 | 152 |
107 | 153 |
108 | 154 |
109 | 155 |
110 | 156 |
111 | 157 |
112 | 160 |
113 | 161 |
114 | 162 |
115 | 163 |
116 | 164 |
117 | 165 |
118 | 166 |
119 | 167 |
120 | 170 |
121 | 171 |
122 | 172 |
123 | 173 |
124 | 174 |
125 | 175 |
126 | 176 |
127 | 177 |
128 | 200 |
Decimal | Octal |
129 | 201 |
130 | 202 |
131 | 203 |
132 | 204 |
133 | 205 |
134 | 206 |
135 | 207 |
136 | 210 |
137 | 211 |
138 | 212 |
139 | 213 |
140 | 214 |
141 | 215 |
142 | 216 |
143 | 217 |
144 | 220 |
145 | 221 |
146 | 222 |
147 | 223 |
148 | 224 |
149 | 225 |
150 | 226 |
151 | 227 |
152 | 230 |
153 | 231 |
154 | 232 |
155 | 233 |
156 | 234 |
157 | 235 |
158 | 236 |
159 | 237 |
160 | 240 |
161 | 241 |
162 | 242 |
163 | 243 |
164 | 244 |
165 | 245 |
166 | 246 |
167 | 247 |
168 | 250 |
169 | 251 |
170 | 252 |
171 | 253 |
172 | 254 |
173 | 255 |
174 | 256 |
175 | 257 |
176 | 260 |
177 | 261 |
178 | 262 |
179 | 263 |
180 | 264 |
181 | 265 |
182 | 266 |
183 | 267 |
184 | 270 |
185 | 271 |
186 | 272 |
187 | 273 |
188 | 274 |
189 | 275 |
190 | 276 |
191 | 277 |
192 | 300 |
Decimal | Octal |
193 | 301 |
194 | 302 |
195 | 303 |
196 | 304 |
197 | 305 |
198 | 306 |
199 | 307 |
200 | 310 |
201 | 311 |
202 | 312 |
203 | 313 |
204 | 314 |
205 | 315 |
206 | 316 |
207 | 317 |
208 | 320 |
209 | 321 |
210 | 322 |
211 | 323 |
212 | 324 |
213 | 325 |
214 | 326 |
215 | 327 |
216 | 330 |
217 | 331 |
218 | 332 |
219 | 333 |
220 | 334 |
221 | 335 |
222 | 336 |
223 | 337 |
224 | 340 |
225 | 341 |
226 | 342 |
227 | 343 |
228 | 344 |
229 | 345 |
230 | 346 |
231 | 347 |
232 | 350 |
233 | 351 |
234 | 352 |
235 | 353 |
236 | 354 |
237 | 355 |
238 | 356 |
239 | 357 |
240 | 360 |
241 | 361 |
242 | 362 |
243 | 363 |
244 | 364 |
245 | 365 |
246 | 366 |
247 | 367 |
248 | 370 |
249 | 371 |
250 | 372 |
251 | 373 |
252 | 374 |
253 | 375 |
254 | 376 |
255 | 377 |
Decimal | Binary | Octal | Hex |
0 | 0000 | 0 | 0 |
1 | 0001 | 1 | 1 |
2 | 0010 | 2 | 2 |
3 | 0011 | 3 | 3 |
4 | 0100 | 4 | 4 |
5 | 0101 | 5 | 5 |
6 | 0110 | 6 | 6 |
7 | 0111 | 7 | 7 |
8 | 1000 | 10 | 8 |
9 | 1001 | 11 | 9 |
10 | 1010 | 12 | A |
11 | 1011 | 13 | B |
12 | 1100 | 14 | C |
13 | 1101 | 15 | D |
14 | 1110 | 16 | E |
15 | 1111 | 17 | F |