HEXADECIMAL & DECIMAL Conversion
Byte - Bit - Nibble - Halfbyte ???
- B Y T E - (Byte = 8-bit)
-------------------
MSD-NIBBLE|LSD-NIBBLE (NIBBLE (Half Byte) = 4-bit)
---------|---------------------------------------------
Bit NUMBER --- 7 6 5 4 | 3 2 1 0 < used for PC/PS-products
(Bit NUMBER --- 0 1 2 3 | 4 5 6 7 < only for LARGE system products)
---------|---------------------------------------------
Bit VALUE --- 8 4 2 1 | 8 4 2 1 | HEX | DECIMAL
---------|-----------|-------|-----------
0 0 0 0 | 0 0 0 0 | 0 | 0
0 0 0 0 | 0 0 0 1 | 1 | 1
0 0 0 0 | 0 0 1 0 | 2 | 2
0 0 0 0 | 0 0 1 1 | 3 | 3
0 0 0 0 | 0 1 0 0 | 4 | 4
0 0 0 0 | 0 1 0 1 | 5 | 5
0 0 0 0 | 0 0 1 1 | 6 | 6
0 0 0 0 | 0 1 1 1 | 7 | 7
0 0 0 0 | 1 0 0 0 | 8 | 8
0 0 0 0 | 1 0 0 1 | 9 | 9
0 0 0 0 | 1 0 1 0 | A | 10
0 0 0 0 | 1 0 1 1 | B | 11
0 0 0 0 | 1 1 0 0 | C | 12
0 0 0 0 | 1 1 0 1 | D | 13
0 0 0 0 | 1 1 1 0 | E | 14
0 0 0 0 | 1 1 1 1 | F | 15
-----------------------------------------
0 0 0 1 | 0 0 0 0 | 10 | 16
0 0 0 1 | 0 0 0 1 | 11 | 17
0 0 0 1 | 0 0 1 0 | 12 | 18
0 0 0 1 | 0 0 1 1 | 13 | 19
~ ~ ~ ~
1 1 1 1 | 1 1 0 1 | FD | 253
1 1 1 1 | 1 1 1 0 | FE | 254
1 1 1 1 | 1 1 1 1 | FF | 255 (max. for 1-byte)
-----------------------------------------
MSD = Most Significant Digit
LSD = Least Significant Digit
HEXADECIMAL & DECIMAL Conversion
From hex: to DECIMAL
Locate each hex digit in it's corresponding column position and note the
decimal equivalents. Add these to obtain the decimal value.
From decimal: to HEX
- Locate the largest decimal value in the table that will fit into the decimal number to be converted, and
- note it's hex equivalent and hex column position.
- Find the decimal remainder. Repeat the process on this and subsequent remainders.
Examples:
BINARY - HEX to DECIMAL conversion
Binary value = 0000 0111 1010 1100 0100 0101 (3-bytes)
HEX value = 0 7 A C 4 5
HalfByte # -> (6 ----- 5 ----- 4 ----- 3 ----- 2 ----- 1)
(HB) 0 + 458.752+40.960+ 3.072 + 64 + 5 = 502.853
DECIMAL to HEX - BINARY conversion
Decimal value = 116.662.538 -> 6
-100.663.296 found in (HalfByte) HB #7
-------------
15.999.242 -> F
-15.728.640 found in HB #6
------------
270.602 -> 4
-262.144 found in HB #5
---------
8.458 -> 2
-8.192 found in HB #4
-------
266 -> 1
-256 found in HB #3
-----
10 -> 0 set to 0 - because no match in HB #2
-----
10 -> A found in (HalfByte) HB #1
HEX '6F4210A' = BINARY 0110 1111 0100 0010 0001 0000 1010 (3,5 - Byte)
+--------------------------------------------------------------------------------+
| WORD |
|--------------------------------------------------------------------------------|
| HALFWORD | HALFWORD |
|----------------------------------------------------|---------------------------|
| BYTE | BYTE | BYTE | BYTE |
|-----------------------------|----------------------|----------------|----------|
|BITs 0123 | 4567 | 0123 | 4567 | 0123 | 4567 | 0123|4567| <- only LARGE System
|---------------|-------------|------------|---------|--------|-------|-----|----|
|BITs 7654 | 3210 | 7654 | 3210 | 7654 | 3210 | 7654|3210| <- PC/PS System
|---------------|-------------|------------|---------|--------|-------|-----|----|
|H| Decimal |H| Decimal |H| Decimal |H| Dec. |H| Dec. |H| Dec.|H| D |H|D |
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
| | 8 | | 7 | | 6 | | 5 | | 4 | | 3 | | 2 | |1 | <- Half-byte (nibble)
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|0| 0 |0| 0 |0| 0 |0| 0 |0| 0 |0| 0 |0| 0 |0| 0|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|1| 268.435.456|1| 16.777.216|1| 1.048.576|1| 65.536|1| 4.096|1| 256|1| 16|1| 1|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|2| 536.870.912|2| 33.554.432|2| 2.097.152|2|131.072|2| 8.192|2| 512|2| 32|2| 2|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|3| 805.306.368|3| 50.331.648|3| 3.145.728|3|196.608|3|12.288|3| 768|3| 48|3| 3|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|4|1.073.741.824|4| 67.108.864|4| 4.194.304|4|262.144|4|16.384|4|1.024|4| 64|4| 4|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|5|1.342.177.280|5| 83.886.080|5| 5.242.880|5|327.680|5|20.480|5|1.280|5| 80|5| 5|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|6|1.610.612.736|6|100.663.296|6| 6.291.456|6|393.216|6|24.576|6|1.536|6| 96|6| 6|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|7|1.879.048.192|7|117.440.512|7| 7.340.032|7|458.752|7|28.672|7|1.792|7|112|7| 7|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|8|2.147.483.648|8|134.217.728|8| 8.388.608|8|524.288|8|32.768|8|2.048|8|128|8| 8|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|9|2.415.919.104|9|150.994.944|9| 9.437.184|9|589.824|9|36.864|9|2.304|9|144|9| 9|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|A|2.684.354.560|A|167.772.160|A|10.485.760|A|655.360|A|40.960|A|2.560|A|160|A|10|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|B|2.952.790.016|B|184.549.376|B|11.534.336|B|720.896|B|45.056|B|2.816|B|176|B|11|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|C|3.221.225.472|C|201.326.592|C|12.582.912|C|786.432|C|49.152|C|3.072|C|192|C|12|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|D|3.489.660.928|D|218.103.808|D|13.631.488|D|851.968|D|53.248|D|3.328|D|208|D|13|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|E|3.758.096.384|E|234.881.024|E|14.680.064|E|917.504|E|57.344|E|3.584|E|224|E|14|
|-|-------------|-|-----------|-|----------|-|-------|-|------|-|-----|-|---|-|--|
|F|4.026.531.840|F|251.658.240|F|15.728.640|F|983.040|F|61.440|F|3.840|F|240|F|15|
|---------------|-------------|------------|---------|--------|-------|-----|----|
| 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | <- Half-byte (nibble)
+--------------------------------------------------------------------------------+
Powers of 2 and 16
| m |
n |
2  m and 16 n |
- |
m |
n |
2 m and 16 n |
0
1
2
3 |
0 |
1
2
4
8 |
- |
32
33
34
35 |
8 |
4 294 967 296
8 589 934 592
17 179 869 184
34 359 738 368 |
4
5
6
7 |
1 |
16
32
64
128 |
- |
32
33
34
35 |
9 |
68 719 476 736
137 438 953 472
274 877 906 944
549 755 813 888 |
8
9
10
11 |
2 |
256
512
1 024
2 048 |
- |
40
41
42
43 |
10 |
1 099 511 627 776
2 199 023 255 552
4 398 046 511 104
8 796 093 022 208 |
12
13
14
15 |
3 |
4 096
8 192
16 384
32 768 |
- |
44
45
46
47 |
11 |
17 592 186 044 416
35 184 372 088 832
70 368 744 177 664
140 737 488 355 328 |
16
17
18
19 |
4 |
65 536
131 072
262 144
524 288 |
- |
48
49
50
51 |
12 |
281 474 976 710 656
562 949 953 421 312
1 125 899 906 842 624
2 251 799 813 685 248 |
20
21
22
23 |
5 |
1 048 576
2 097 152
4 194 304
8 388 608 |
- |
52
53
54
55 |
13 |
4 503 599 627 370 496
9 007 199 254 740 992
18 014 398 509 481 984
36 028 797 018 963 968 |
24
25
26
27 |
6 |
16 777 216
33 554 432
67 108 864
134 217 728 |
- |
56
57
58
59 |
14 |
72 057 594 037 927 936
144 115 188 075 885 872
288 230 376 151 711 744
576 460 752 303 423 488 |
28
29
30
31 |
7 |
268 435 456
536 870 912
1 073 741 824
2 147 483 648 |
- |
60
61
62
63 |
15 |
1 152 921 504 606 846 976
2 305 843 009 213 693 952
4 611 686 018 427 387 904
9 223 372 036 854 775 808 |
| Symbol |
Value |
| K (kilo) |
1.024=2 10 |
| M (mega) |
1.048.576=2 20 |
| G (giga) |
1.073.741.824=2 30 |
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