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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.
.

-

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-long word organization,
showing address space vs.
numbered bit lines.

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      Powers of 2 Table

Bit
Line
#
 Power
of 2
Expo-
nent
Binary
Bit Weight
in Decimal
Highest Number Count
(Memory Address)
Computer Hardware
Address Organization
Decimal
Hex
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

 Second
byte

(16 lines
can count
to 65,535)

10

29
512

1,023

0000 03FF

11

210
1,024

2,047

0000 07FF

12

211
2,048

4,095

0000 0FFF

13

212
4,096

8,191

0000 1FFF

14

213
8,192

16,383

0000 3FFF

15

214
16,384

32,767

0000 7FFF

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)
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 Giga-bytes)

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 47 Billion pages indexed. So, no "wall".

50

60

130 - 680

120

90

90

70

70


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     Powers of 2 Table (con't.)

Bit
Line
#
 Power
of 2
Expo-
nent
Binary
Bit Weight
in Decimal
Highest Number Count
(Memory Address)
Computer Hardware
Address Organization
Decimal
Binary
Bytes
Words
33
232

4,294,967,296

8,589,934,591

-

 Fifth
byte
(40 lines)

 Third
word

(48 bits)
34
233

8,589,934,592

17,179,869,183

35
234

17,179,869,184

34,359,738,367

36
235

34,359,738,368

68,719,476,735

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

2,199,023,255,552

4,398,046,511,103

43

242

4,398,046,511,104

8,796,093,022,207

44

243

8,796,093,022,208

17,592,186,044,415

45

244
18 Trillion

35,184,372,088,831

46

245
35 Trillion

70,368,744,177,663

47

246
70 Trillion

140,737,488,355,327

48

247
140 Trillion

281,474,976,710,655

49
248
281 Trillion

562,949,953,421,311

-

Seventh
Byte
(56 lines)
 Fourth
word

(64 bits)
50
249
563 Trillion

1,125,899,906,842,623

51
250
One Quadrillion

2,251,799,813,685,247

52
251
2 Quadrillion

4,503,599,627,370,495

53
252
4 Quadrillion

9,007,199,254,740,991

54
253
9 Quadrillion

18,014,398,509,481,983

55
254
18 Quadrillion

36,028,797,018,963,967

56
255
36 Quadrillion

72,057,594,037,927,935

57

256
72 Quadrillion

144,115,188,075,855,871

-

 Eighth
byte
(64 lines)

58

257
144 Quadrillion

288,230,376,151,711,743

59

258
288 Quadrillion

576,460,752,303,423,487

60

259
576 Quadrillion

1,152,921,504,606,846,975

61

260
One Quintillion

2,305,843,009,213,693,951

62

261
Two Quintillion

4,611,686,018,427,387,903

63

262

9,223,372,036,854,775,807

(63 lines can count to 9.2 quintillion)

64

263

18,446,744,073,709,551,615

(64 lines can count to 18.4 quintillion)
64-bit machine limitation

-

 
  Why fool around with this silly page?
  Why not go to the REAL AUTHORITY -
  
  Power of Two - Wikipedia
  

  Which goes up to the 95th power - 295

  Many thanks to Contributing Editor
  Robert Rolf
  for pointing out errors on this page,
  which have all been fixed
  (I think, and I hope).
.

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50

60

130 - 680

120

90

90

70

70



DISCLAIMER:
Any reported errors will be fixed.

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

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This Vaughns Powers-of-Two Table
was last updated on 2020-05-31.