Lists of the Powers of 2, 8 and 16

=== by Bob Sutherland ===

Please read my web page A Quick Review of Powers, Exponents and Scientific Notation if you need help with any of the vocabulary or math symbols.

The binary number system is based on the powers of 2. The octal number system is based on the powers of 8. The hexadecimal number system is based on the powers of 16. Many technical specifications in the design of computers are based on these three number systems and the following charts.

This web page contains six charts. Go to End↓

Powers of 2 : 2n

20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512
210 = 1024
211 = 2048
212 = 4096
213 = 8192
214 = 16384
215 = 32768
216 = 65536
217 = 131072
218 = 262144
219 = 524288
220 = 1048576
221 = 2097152
222 = 4194304
223 = 8388608
224 = 16777216
225 = 33554432
226 = 67108864
227 = 134217728
228 = 268435456
229 = 536870912
230 = 1073741824
231 = 2147483648
232 = 4294967296
233 = 8589934592
234 = 17179869184
235 = 34359738368
236 = 68719476736
237 = 137438953472
238 = 274877906944
239 = 549755813888
240 = 1099511627776
241 = 2199023255552
242 = 4398046511104
243 = 8796093022208
244 = 17592186044416
245 = 35184372088832
246 = 70368744177664
247 = 140737488355328
248 = 281474976710656
249 = 562949953421312
250 = 1125899906842624
251 = 2251799813685248
252 = 4503599627370496
253 = 9007199254740992

2n - 1

One less than a power of 2. These numbers often appear as a maximum size in computer technical specifications.

20 - 1 = 0
21 - 1 = 1
22 - 1 = 3
23 - 1 = 7
24 - 1 = 15
25 - 1 = 31
26 - 1 = 63
27 - 1 = 127
28 - 1 = 255
29 - 1 = 511
210 - 1 = 1023
211 - 1 = 2047
212 - 1 = 4095
213 - 1 = 8191
214 - 1 = 16383
215 - 1 = 32767
216 - 1 = 65535
217 - 1 = 131071
218 - 1 = 262143
219 - 1 = 524287
220 - 1 = 1048575
221 - 1 = 2097151
222 - 1 = 4194303
223 - 1 = 8388607
224 - 1 = 16777215
225 - 1 = 33554431
226 - 1 = 67108863
227 - 1 = 134217727
228 - 1 = 268435455
229 - 1 = 536870911
230 - 1 = 1073741823
231 - 1 = 2147483647
232 - 1 = 4294967295
233 - 1 = 8589934591
234 - 1 = 17179869183
235 - 1 = 34359738367
236 - 1 = 68719476735
237 - 1 = 137438953471
238 - 1 = 274877906943
239 - 1 = 549755813887
240 - 1 = 1099511627775
241 - 1 = 2199023255551
242 - 1 = 4398046511103
243 - 1 = 8796093022207
244 - 1 = 17592186044415
245 - 1 = 35184372088831
246 - 1 = 70368744177663
247 - 1 = 140737488355327
248 - 1 = 281474976710655
249 - 1 = 562949953421311
250 - 1 = 1125899906842623
251 - 1 = 2251799813685247
252 - 1 = 4503599627370495
253 - 1 = 9007199254740991

Powers of 8 : 8n

80 = 1
81 = 8
82 = 64
83 = 512
84 = 4096
85 = 32768
86 = 262144
87 = 2097152
88 = 16777216
89 = 134217728
810 = 1073741824
811 = 8589934592
812 = 68719476736
813 = 549755813888
814 = 4398046511104
815 = 35184372088832
816 = 281474976710656
817 = 2251799813685248

8n - 1

One less than a power of 8. These numbers often appear as a maximum size in computer technical specifications.

80 - 1 = 0
81 - 1 = 7
82 - 1 = 63
83 - 1 = 511
84 - 1 = 4095
85 - 1 = 32767
86 - 1 = 262143
87 - 1 = 2097151
88 - 1 = 16777215
89 - 1 = 134217727
810 - 1 = 1073741823
811 - 1 = 8589934591
812 - 1 = 68719476735
813 - 1 = 549755813887
814 - 1 = 4398046511103
815 - 1 = 35184372088831
816 - 1 = 281474976710655
817 - 1 = 2251799813685247

Powers of 16 : 16n

160 = 1
161 = 16
162 = 256
163 = 4096
164 = 65536
165 = 1048576
166 = 16777216
167 = 268435456
168 = 4294967296
169 = 68719476736
1610 = 1099511627776
1611 = 17592186044416
1612 = 281474976710656
1613 = 4503599627370496

16n - 1

One less than a power of 16. These numbers often appear as a maximum size in computer technical specifications.

160 - 1 = 0
161 - 1 = 15
162 - 1 = 255
163 - 1 = 4095
164 - 1 = 65535
165 - 1 = 1048575
166 - 1 = 16777215
167 - 1 = 268435455
168 - 1 = 4294967295
169 - 1 = 68719476735
1610 - 1 = 1099511627775
1611 - 1 = 17592186044415
1612 - 1 = 281474976710655
1613 - 1 = 4503599627370495