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Number ranges and bits

These may be handy when you loose count. I loose count all the time, so I made this page.

Numbers

The basics.

Octal, decimal, hexadecimal and binary
Oct Dec Hex Bin
000 000000
001 110001
002 220010
003 330011
004 440100
005 550101
006 660110
007 770111
010 881000
011 991001
01210A1010
01311B1011
01412C1100
01513D1101
01614E1110
01715F1111

See: Octal, Hexadecimal and Decimal to hexadecimal table.

Number ranges

Number ranges per hex digit.
The first column shows the number of bits in the 2nd last column.
The last column shows the value divided by 2¹⁰ (k) or 2²⁰ (M).
To improve legibility, hex digits and bits are grouped per four digits.

Hexadecimal number ranges and their octal, decimal, hexadecimal and binary values
Bits Hex range Octal Unsigned
decimal
HexBinary k or
M
 4 1 - F 001 1 1 0001
017 15 F 1111
 8 10 - FF 020 16 10 0001 0000
0377 255 FF 1111 1111
12 100 - FFF 0400 256 100 0001  0000 0000
07777 4095 FFF 1111  1111 1111
16 1000 - FFFF 010000 4096 1000 0001 0000  0000 0000 4 k
0177777 65535 FFFF 1111 1111  1111 1111
20 1 0000 - F FFFF 0200000 65536 1 0000 0001  0000 0000  0000 0000 64 k
03777777 1048575 F FFFF 1111  1111 1111  1111 1111
24 10 0000 - FF FFFF 04000000 1048576 10 0000 0001 0000  0000 0000  0000 0000 1 M
077777777 16777215 FF FFFF 1111 1111  1111 1111  1111 1111
28 100 0000 - FFF FFFF 0100000000 16777216 100 0000 0001  0000 0000  0000 0000  0000 0000 16 M
01777777777 268435455 FFF FFFF 1111  1111 1111  1111 1111  1111 1111
32 1000 0000 - FFFF FFFF 02000000000 268435456 1000 0000 0001 0000  0000 0000  0000 0000  0000 0000 256 M
037777777777 4294967295 FFFF FFFF 1111 1111  1111 1111  1111 1111  1111 1111

The next entry in the above table would be the 4G to 64G - 1 range.

Boundaries

The biggest binary - round 32-bit signed positive number:

Octal Signed
decimal
Hex Binary
010000000000  1073741824 4000 0000 0100 0000  0000 0000  0000 0000  0000 000

The biggest 32-bit signed positive number:

Octal Signed
decimal
Hex Binary
017777777777  2147483647 7FFF FFFF 0111 1111  1111 1111  1111 1111  1111 1111

The most negative 32-bit signed number:

Octal Signed
decimal
Hex Binary
020000000000 -2147483648 8000 0000 1000 0000  0000 0000  0000 0000  0000 0000

And the least negative 32-bit signed number:

Octal Signed
decimal
Hex Binary
037777777777          -1 FFFF FFFF 1111 1111  1111 1111  1111 1111  1111 1111

So 32-bit hex numbers > '7FFF FFFF' may be negative. These are part of the '1000 0000' to 'FFFF FFFF' range.
For 64-bit numbers just double the width: A 64-bit '-1' is '0xFFFFFFFFFFFFFFFF';

The biggest binary - round 64-bit signed positive number:4000 0000 0000 0000
The biggest 64-bit signed positive number:7FFF FFFF FFFF FFFF
The most negative 64-bit signed number:8000 0000 0000 0000
The least negative 64-bit signed number:FFFF FFFF FFFF FFFF

Bits

Individual bits and their octal, decimal and hexadecimal values;
For instance, 2⁰ = 1 and 2³¹ = 2147483648 or 0x80000000.
The last column shows the value divided by 2¹⁰ (k), 2²⁰ (M), or 2³⁰ (G).
To improve legibility, hex digits and bits are grouped per four digits.

Individual bits and their octal, decimal, hexadecimal and binary values
Bit Octal Unsigned
decimal
Hex Binary k, M
or G
0 001 1 1 0001
1 002 2 2 0010
2 004 4 4 0100
3 010 8 8 1000
4 020 16 10 0001 0000
5 040 32 20 0010 0000
6 0100 64 40 0100 0000
7 0200 128 80 1000 0000
8 0400 256 100 0001  0000 0000
9 01000 512 200 0010  0000 0000
10 02000 1024 400 0100  0000 0000 1 k
11 04000 2048 800 1000  0000 0000 2 k
12 010000 4096 1000 0001 0000  0000 0000 4 k
13 020000 8192 2000 0010 0000  0000 0000 8 k
14 040000 16384 4000 0100 0000  0000 0000 16 k
15 0100000 32768 8000 1000 0000  0000 0000 32 k
16 0200000 65536 1 0000 0001  0000 0000  0000 0000 64 k
17 0400000 131072 2 0000 0010  0000 0000  0000 0000 128 k
19 01000000 262144 4 0000 0100  0000 0000  0000 0000 256 k
19 02000000 524288 8 0000 1000  0000 0000  0000 0000 512 k
20 04000000 1048576 10 0000 0001 0000  0000 0000  0000 0000 1 M
21 010000000 2097152 20 0000 0010 0000  0000 0000  0000 0000 2 M
22 020000000 4194304 40 0000 0100 0000  0000 0000  0000 0000 4 M
23 040000000 8388608 80 0000 1000 0000  0000 0000  0000 0000 8 M
24 0100000000 16777216 100 0000 0001  0000 0000  0000 0000  0000 0000 16 M
25 0200000000 33554432 200 0000 0010  0000 0000  0000 0000  0000 0000 32 M
26 0400000000 67108864 400 0000 0100  0000 0000  0000 0000  0000 0000 64 M
27 01000000000 134217728 800 0000 1000  0000 0000  0000 0000  0000 0000 128 M
28 02000000000 268435456 1000 0000 0001 0000  0000 0000  0000 0000  0000 0000 256 M
29 04000000000 536870912 2000 0000 0010 0000  0000 0000  0000 0000  0000 0000 512 M
30 010000000000 1073741824 4000 0000 0100 0000  0000 0000  0000 0000  0000 0000 1 G
31 020000000000 2147483648 8000 0000 1000 0000  0000 0000  0000 0000  0000 0000 2 G

64-bit

I don't think anyone uses octal or decimal in these ranges.
The 3rd and 6st column show the value divided by 2³⁰ (G), 2⁴⁰ (T), 2⁵⁰ (P) or 2⁶⁰ (E).

Individual bits and their hexadecimal values
Bit Hex G or T Bit Hex T, P
or E
32 1 0000 0000 4 G 48 1 0000 0000 0000256 T
33 2 0000 0000 8 G 49 2 0000 0000 0000512 T
34 4 0000 000016 G 50 4 0000 0000 0000 1 P
35 8 0000 000032 G 51 8 0000 0000 0000 2 P
36 10 0000 000064 G 52 10 0000 0000 0000 4 P
37 20 0000 0000128 G 53 20 0000 0000 0000 8 P
38 40 0000 0000256 G 54 40 0000 0000 000016 P
39 80 0000 0000512 G 55 80 0000 0000 000032 P
40 100 0000 0000 1 T 56 100 0000 0000 000064 P
41 200 0000 0000 2 T 57 200 0000 0000 0000128 P
42 400 0000 0000 4 T 58 400 0000 0000 0000256 P
43 800 0000 0000 8 T 59 800 0000 0000 0000512 P
44 1000 0000 000016 T 60 1000 0000 0000 00001 E
45 2000 0000 0000 32 T 61 2000 0000 0000 00002 E
46 4000 0000 0000 64 T 62 4000 0000 0000 00004 E
47 8000 0000 0000128 T 63 8000 0000 0000 00008 E

The next entry in the above table would be 16 E.