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Computer Math

Powers of 2 Table
(This page is NOT suitable
for small screens.)

by Vaughn Aubuchon

Here is a brief summary chart illustrating the mathematical powers of two, shown in binary, decimal, and hexadecimal notation.

Here is this file in Adobe Acrobat format - powers-of-2.pdf
The table goes up to the 64th power of two.
This power-of-2 chart is grouped into 8-bit-long computer bytes and 16-bit word organization, showing address space vs. numbered bit lines.

300

140

Powers of 2 Table

Bit
Line
Number
 Powers
of 2
Exponent
Binary
Bit Weight
in Decimal
Highest Number Count
(Memory Address)
Computer Hardware
Address Organization
Decimal
Hexadecimal
Binary
Bytes
Words
1
20
1
1
0001
0000 0001
 First byte
(8 lines
can count
to 255)
 First word
(16 bits)

(if little
endian)
2
21
2
3
0003
0000 0011
3
22
4
7
0007
0000 0111
4
23
8
15
000F
0000 1111
5
24
16
31
001F
0001 1111
6
25
32
63
003F
0011 1111
7
26
64
127
007F
0111 1111
8
27
128
255
00FF
1111 1111

9

28

256

511

0000 01FF

0001 1111 1111

 Second byte
(16 lines
can count
to 65,535)

10

29

512

1,023

0000 03FF

0011 1111 1111

11

210

1,024

2,047

0000 07FF

0111 1111 1111

12

211

2,048

4,095

0000 0FFF

1111 1111 1111

13

212

4,096

8,191

0000 1FFF

etc.

14

213

8,192

16,383

0000 3FFF

etc.

15

214

16,384

32,767

0000 7FFF

etc.

16

215

32,768

65,535

0000 FFFF

-

17
216
65,536
 131,071
0001 FFFF

-

 Third byte
(24 lines
can count
to 16.7M)
 Second
word

(32 bits)

(if little
endian)









32-bit
machine
limitation
18
217
131,072
 262,143
0003 FFFF
19
218
262,144
 524,287
0007 FFFF
20
219
524,288
1,048,575
000F FFFF
21
220
1,048,576
 2,097,151
001F FFFF
22
221
2,097,152
 4,194,303
003F FFFF
23
222
4,194,304
 8,388,607
007F FFFF
24
223
8,388,608
16,777,215
00FF FFFF

25

224

16,777,216

 33,554,431

01FF FFFF

-

 Fourth byte
(32 lines
can count
to 4.2B)
(4 Gigabytes)

26

225

33,554,432

 67,108,863

03FF FFFF

27

226

67,108,864

134,217,727

07FF FFFF

28

227

134,217,728

268,435,455

0FFF FFFF

29

228

268,435,456

 536,870,911

1FFF FFFF

30

229

536,870,912

 1,073,741,823

3FFF FFFF

31

230

1,073,741,824

 2,147,483,647

7FFF FFFF

32

231

2,147,483,648

4,294,967,295

FFFF FFFF

This is the 32-bit machine addressing limitation, unless double-words or extra bits are used.
Although a reputed "Google wall", regarding the number of web pages that can be indexed,
Google now reports over 2 Billion pages indexed.

33
232
4,294,967,296
8,589,934,591
etc.

-

 Fifth byte
(40 lines)

 Third
word

(48 bits)
34
233
8,589,934,592
17,179,869,183
etc.
35
234
17,179,869,184
34,359,738,367
etc.
36
235
34,359,738,368
68,719,476,735
etc.
37
236
68,719,476,736
137,438,953,471

-

38
237
137,438,953,472
274,877,906,943
39
238
274,877,906,944
549,755,813,887
40
239
549,755,813,888
1,099,511,627,775

41

240

1,099,511,627,776

2,199,023,255,551

 -

-

 Sixth byte
(48 lines)

42

241

2 Trillion

4,398,046,511,103

43

242

4 Trillian

etc.

44

243

9 Trillion

etc.

45

244

18 Trillion

-

46

245

35 Trillion

-

47

246

70 Trillion

70,368,744,177,664

48

247

140 Trillion

-

49
248

281 Trillion

-

-

-

Seventh Byte
(56 lines)
 Fourth
word

(64 bits)

















64-bit
machine
limitation
50
249

563 Trillion

-

51
250

One Quadrillion

-

52
251

2 Quadrillion

-

53
252

4 Quadrillion

-

54
253

9 Quadrillion

-

55
254

18 Quadrillion

18,014,398,509,482,000

56
255

36 Quadrillion

-

57

256

72 Quadrillion

-

-

-

 Eighth byte
(64 lines)

58

257

144 Quadrillion

-

59

258

288 Quadrillion

-

60

259

576 Quadrillion

-

61

260

One Quintillion

-

62

261

Two Quintillion

-

63

262

(63 lines can count to 4.6 quintillion)
4,611,686,018,4xx,xxx,xxx
4.6 x 1018
(approx. weight of the EARTH in Tons)

64

263

9.2 quintillion

(64 lines can count to 9.2 quintillion)
9,223,372,036,xxx,xxx,xxx

50

60

120- 770

110

100

110

90

80

DISCLAIMER
Although the author has tried to be as accurate as possible, errors are possible.
I could not find an online chart like the above. So, I made this Powers of 2 Chart, to help myself visualize the inner workings of a data computer. I hope that it helps you.

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Tags: powers-of-2 table, computer byte values


Vaughn Aubuchon
Vaughn's Summaries
©2003, 2004, 2007 Vaughn Aubuchon
www.vaughns-1-pagers.com
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This Vaughns Powers-of-Two Table
was last updated on 2014-10-29.