Powers of 2 Table - Vaughn's Summaries

Vaughn's Summaries *Computer Summaries* *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. .	-
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. Here is this file in Adobe Acrobat format - powers-of-2.pdf .

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
Bit Line Number	Powers of 2 Exponent	Binary Bit Weight in Decimal	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 47 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 Trillion	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	130 - 710	130	90	90	70	70

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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This Vaughns Powers-of-Two Table
was last updated on 2018-05-31.