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Binary, Octal and Hexadecimal Numbers

Decimal, binary, octal and hexadecimal numbers.

Binary, Octal and Hexadecimal Numbers
Denary
(base 10)
Hexadecimal
(base 16)
Octal
(base 8)
Binary
(base 2)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
000
001
002
003
004
005
006
007
010
011
012
013
014
015
016
017
00000000
00000001
00000010
00000011
00000100
00000101
00000110
00000111
00001000
00001001
00001010
00001011
00001100
00001101
00001110
00001111
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
10
11
12
13
14
15
16
17
18
19
1A
1B
1C
1D
1E
1F
020
021
022
023
024
025
026
027
030
031
032
033
034
035
036
037
00010000
00010001
00010010
00010011
00010100
00010101
00010110
00010111
00011000
00011001
00011010
00011011
00011100
00011101
00011110
00011111
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
20
21
22
23
24
25
26
27
28
29
2A
2B
2C
2D
2E
2F
040
041
042
043
044
045
046
047
050
051
052
053
054
055
056
057
00100000
00100001
00100010
00100011
00100100
00100101
00100110
00100111
00101000
00101001
00101010
00101011
00101100
00101101
00101110
00101111
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
30
31
32
33
34
35
36
37
38
39
3A
3B
3C
3D
3E
3F
060
061
062
063
064
065
066
067
070
071
072
073
074
075
076
077
00110000
00110001
00110010
00110011
00110100
00110101
00110110
00110111
00111000
00111001
00111010
00111011
00111100
00111101
00111110
00111111
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
40
41
42
43
44
45
46
47
48
49
4A
4B
4C
4D
4E
4F
100
101
102
103
104
105
106
107
110
111
112
113
114
115
116
117
01000000
01000001
01000010
01000011
01000100
01000101
01000110
01000111
01001000
01001001
01001010
01001011
01001100
01001101
01001110
01001111
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
50
51
52
53
54
55
56
57
58
59
5A
5B
5C
5D
5E
5F
120
121
122
123
124
125
126
127
130
131
132
133
134
135
136
137
01010000
01010001
01010010
01010011
01010100
01010101
01010110
01010111
01011000
01011001
01011010
01011011
01011100
01011101
01011110
01011111
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
60
61
62
63
64
65
66
67
68
69
6A
6B
6C
6D
6E
6F
140
141
142
143
144
145
146
147
150
151
152
153
154
155
156
157
01100000
01100001
01100010
01100011
01100100
01100101
01100110
01100111
01101000
01101001
01101010
01101011
01101100
01101101
01101110
01101111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
70
71
72
73
74
75
76
77
78
79
7A
7B
7C
7D
7E
7F
160
161
162
163
164
165
166
167
170
171
172
173
174
175
176
177
01110000
01110001
01110010
01110011
01110100
01110101
01110110
01110111
01111000
01111001
01111010
01111011
01111100
01111101
01111110
01111111
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
80
81
82
83
84
85
86
87
88
89
8A
8B
8C
8D
8E
8F
200
201
202
203
204
205
206
207
210
211
212
213
214
215
216
217
10000000
10000001
10000010
10000011
10000100
10000101
10000110
10000111
10001000
10001001
10001010
10001011
10001100
10001101
10001110
10001111
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
90
91
92
93
94
95
96
97
98
99
9A
9B
9C
9D
9E
9F
220
221
222
223
224
225
226
227
230
231
232
233
234
235
236
237
10010000
10010001
10010010
10010011
10010100
10010101
10010110
10010111
10011000
10011001
10011010
10011011
10011100
10011101
10011110
10011111
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
A0
A1
A2
A3
A4
A5
A6
A7
A8
A9
AA
AB
AC
AD
AE
AF
240
241
242
243
244
245
246
247
250
251
252
253
254
255
256
257
10100000
10100001
10100010
10100011
10100100
10100101
10100110
10100111
10101000
10101001
10101010
10101011
10101100
10101101
10101110
10101111
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
B0
B1
B2
B3
B4
B5
B6
B7
B8
B9
BA
BB
BC
BD
BE
BF
260
261
262
263
264
265
266
267
270
271
272
273
274
275
276
277
10110000
10110001
10110010
10110011
10110100
10110101
10110110
10110111
10111000
10111001
10111010
10111011
10111100
10111101
10111110
10111111
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
C0
C1
C2
C3
C4
C5
C6
C7
C8
C9
CA
CB
CC
CD
CE
CF
300
301
302
303
304
305
306
307
310
311
312
313
314
315
316
317
11000000
11000001
11000010
11000011
11000100
11000101
11000110
11000111
11001000
11001001
11001010
11001011
11001100
11001101
11001110
11001111
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
D0
D1
D2
D3
D4
D5
D6
D7
D8
D9
DA
DB
DC
DD
DE
DF
320
321
322
323
324
325
326
327
330
331
332
333
334
335
336
337
11010000
11010001
11010010
11010011
11010100
11010101
11010110
11010111
11011000
11011001
11011010
11011011
11011100
11011101
11011110
11011111
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
E0
E1
E2
E3
E4
E5
E6
E7
E8
E9
EA
EB
EC
ED
EE
EF
340
341
342
343
344
345
346
347
350
351
352
353
354
355
356
357
11100000
11100001
11100010
11100011
11100100
11100101
11100110
11100111
11101000
11101001
11101010
11101011
11101100
11101101
11101110
11101111
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
F0
F1
F2
F3
F4
F5
F6
F7
F8
F9
FA
FB
FC
FD
FE
FF
360
361
362
363
364
365
366
367
370
371
372
373
374
375
376
377
11110000
11110001
11110010
11110011
11110100
11110101
11110110
11110111
11111000
11111001
11111010
11111011
11111100
11111101
11111110
11111111
  • Denary - the Denary number system (decimal) is a base 10 number system used by people with 10 unique digits 0 to 9
  • Octal - the Octal numeral system (Oct) is a base 8 number system that use the digits 0 to 7
  • Hexadecimal - the Hexadecimal number system (Hex) is a base 16 number system using number 0 - 9 and letters A - F
  • Binary - the Binary number system (Bin) is a base 2 number system using number 1 and 0

Binary to Decimal Conversion

The decimal numbering system has a radix of 10.

A denary (decimal) number can be expressed as

10.5 

= 1 x 101 + 0 x 100 + 5 x 10-1 

The binary numbering system has a radix of 2.

A binary number can be expressed as

1011.1 

= 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20 + 1 x 2-1

= 8 + 0 + 1 + 1 + 1/2 

= 10.5

The distinction binary vs. denary numbers can be indicated as

1011.12 = 10.510

Hexadecimal to Decimal Conversion

The hexadecimal numbering system has a radix of 16 and uses the following 16 distinct digits

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F

'A' corresponds to 10 in the denary system, B to 11, C to 12 ...

A hexadecimal number can be expressed as

1BC 

= 1 x 162 + C x 161 + F x 160

= 1 x 162 + 12 x 161 + 15 x 160

= 256 + 192 + 15

= 463

Related Topics

  • Mathematics

    Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

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  • The Engineering ToolBox (2011). Binary, Octal and Hexadecimal Numbers. [online] Available at: https://www.engineeringtoolbox.com/binary-octal-hexadecimal-numbers-d_1802.html [Accessed Day Month Year].

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11.25.10

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