Hexadecimale talsystem

Det hexadecimale talsystem er baseret på basen 16, hvor vi i 10-talsystemet regner med basen 10. For betegnelsen base benyttes også ordene grundtal eller radix. Radixet eller grundtallet angives ved at skrive det nedenfor tallet. De ekstra cifre (udover 0 – 9) udgøres af bogstaverne A-F, således at A16=1010, B16=1110, C16=1210, D16=1310, E16=1410, F16=1510.


0hex = 0dec = 0oct 0 0 0 0
1hex = 1dec = 1oct 0 0 0 1
2hex = 2dec = 2oct 0 0 1 0
3hex = 3dec = 3oct 0 0 1 1
4hex = 4dec = 4oct 0 1 0 0
5hex = 5dec = 5oct 0 1 0 1
6hex = 6dec = 6oct 0 1 1 0
7hex = 7dec = 7oct 0 1 1 1
8hex = 8dec = 10oct 1 0 0 0
9hex = 9dec = 11oct 1 0 0 1
Ahex = 10dec = 12oct 1 0 1 0
Bhex = 11dec = 13oct 1 0 1 1
Chex = 12dec = 14oct 1 1 0 0
Dhex = 13dec = 15oct 1 1 0 1
Ehex = 14dec = 16oct 1 1 1 0
Fhex = 15dec = 17oct 1 1 1 1

Som i alle positionstalsystemer er – når det angår heltal – pladsen længst til højre 'enerne' (160 – (pr. definition giver et tal opløftet i nulte potens altid 1). Således er 160 = 1). Den næste plads (som vi i titalssystemet kender som 10'erne) er så 'sekstenerne' (161). Derefter er det 'tohundredeseksoghalvtredserne' (162) på den plads hvor 100'erne (102) befinder sig i titalssystemet. På den fjerde plads kommer 'firetusindogseksoghalvfemserne' (163) og så fremdeles.

Eksempler:

Hexadecimal ...udregnet (vha. decimaltal) Decimal ...udregnet
0A16 = 0*161 + 10*160 = 1010 = 1*101 + 0*100
1016 = 1*161 + 0*160 = 1610 = 1*101 + 6*100
2216 = 2*161 + 2*160 = 3410 = 3*101 + 4*100
FF16 = 15*161 + 15*160 = 25510 = 2*102 + 5*101 + 5*100
CF516 = 12*162 + 15*161 + 5*160 = 331710 = 3*103 + 3*102 + 1*101 + 7*100
60D316 = 6*163 + 0*162 + 13*161 + 3*160 = 2478710 = 2*104 + 4*103 + 7*102 + 8*101 + 7*100

Talsystemet bruges i computerne, der dybest set arbejder i det binære talsystem (2-talsystemet, der kun har cifrene 0 og 1). Fidusen er, at med 4 pladser i 2-talsystemet kan man tælle op til 15 (F i hex), så med 8 pladser (8 bits) kan man gå op til FF(hex). Disse 8 bits er lig 1 byte.


Tallene fra 010 til 25510 angivet i hexadecimal
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F
30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F
40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F
50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F
60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F
70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F
80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F
90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F
A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB AC AD AE AF
B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 BA BB BC BD BE BF
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF
D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 DA DB DC DD DE DF
E0 E1 E2 E3 E4 E5 E6 E7 E8 E9 EA EB EC ED EE EF
F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA FB FC FD FE FF


Omregningstabel fra det hexadecimale talsystem til det decimale talsystem

0 1 2 3 4 5 6 7 8 9 A B C D E F
0_16 010 110 210 310 410 510 610 710 810 910 1010 1110 1210 1310 1410 1510
1_16 1610 1710 1810 1910 2010 2110 2210 2310 2410 2510 2610 2710 2810 2910 3010 3110
2_16 3210 3310 3410 3510 3610 3710 3810 3910 4010 4110 4210 4310 4410 4510 4610 4710
3_16 4810 4910 5010 5110 5210 5310 5410 5510 5610 5710 5810 5910 6010 6110 6210 6310
4_16 6410 6510 6610 6710 6810 6910 7010 7110 7210 7310 7410 7510 7610 7710 7810 7910
5_16 8010 8110 8210 8310 8410 8510 8610 8710 8810 8910 9010 9110 9210 9310 9410 9510
6_16 9610 9710 9810 9910 10010 10110 10210 10310 10410 10510 10610 10710 10810 10910 11010 11110
7_16 11210 11310 11410 11510 11610 11710 11810 11910 12010 12110 12210 12310 12410 12510 12610 12710
8_16 12810 12910 13010 13110 13210 13310 13410 13510 13610 13710 13810 13910 14010 14110 14210 14310
9_16 14410 14510 14610 14710 14810 14910 15010 15110 15210 15310 15410 15510 15610 15710 15810 15910
A_16 16010 16110 16210 16310 16410 16510 16610 16710 16810 16910 17010 17110 17210 17310 17410 17510
B_16 17610 17710 17810 17910 18010 18110 18210 18310 18410 18510 18610 18710 18810 18910 19010 19110
C_16 19210 19310 19410 19510 19610 19710 19810 19910 20010 20110 20210 20310 20410 20510 20610 20710
D_16 20810 20910 21010 21110 21210 21310 21410 21510 21610 21710 21810 21910 22010 22110 22210 22310
E_16 22410 22510 22610 22710 22810 22910 23010 23110 23210 23310 23410 23510 23610 23710 23810 23910
F_16 24010 24110 24210 24310 24410 24510 24610 24710 24810 24910 25010 25110 25210 25310 25410 25510

Omregningstabel fra det decimale talsystem til det hexadecimale talsystem

0 1 2 3 4 5 6 7 8 9
0_10 016 116 216 316 416 516 616 716 816 916
1_10 A16 B16 C16 D16 E16 F16 1016 1116 1216 1316
2_10 1416 1516 1616 1716 1816 1916 1A16 1B16 1C16 1D16
3_10 1E16 1F16 2016 2116 2216 2316 2416 2516 2616 2716
4_10 2816 2916 2A16 2B16 2C16 2D16 2E16 2F16 3016 3116
5_10 3216 3316 3416 3516 3616 3716 3816 3916 3A16 3B16
6_10 3C16 3D16 3E16 3F16 4016 4116 4216 4316 4416 4516
7_10 4616 4716 4816 4916 4A16 4B16 4C16 4D16 4E16 4F16
8_10 5016 5116 5216 5316 5416 5516 5616 5716 5816 5916
9_10 5A16 5B16 5C16 5D16 5E16 5F16 6016 6116 6216 6316
10_10 6416 6516 6616 6716 6816 6916 6A16 6B16 6C16 6D16
11_10 6E16 6F16 7016 7116 7216 7316 7416 7516 7616 7716
12_10 7816 7916 7A16 7B16 7C16 7D16 7E16 7F16 8016 8116
13_10 8216 8316 8416 8516 8616 8716 8816 8916 8A16 8B16
14_10 8C16 8D16 8E16 8F16 9016 9116 9216 9316 9416 9516
15_10 9616 9716 9816 9916 9A16 9B16 9C16 9D16 9E16 9F16
16_10 A016 A116 A216 A316 A416 A516 A616 A716 A816 A916
17_10 AA16 AB16 AC16 AD16 AE16 AF16 B016 B116 B216 B316
18_10 B416 B516 B616 B716 B816 B916 BA16 BB16 BC16 BD16
19_10 BE16 BF16 C016 C116 C216 C316 C416 C516 C616 C716
20_10 C816 C916 CA16 CB16 CC16 CD16 CE16 CF16 D016 D116
21_10 D216 D316 D416 D516 D616 D716 D816 D916 DA16 DB16
22_10 DC16 DD16 DE16 DF16 E016 E116 E216 E316 E416 E516
23_10 E616 E716 E816 E916 EA16 EB16 EC16 ED16 EE16 EF16
24_10 F016 F116 F216 F316 F416 F516 F616 F716 F816 F916
25_10 FA16 FB16 FC16 FD16 FE16 FF16 - - - -

Se også

Talord

Hex-systemet har ingen faste talord, men langt de fleste bruger det græske alfabet til at sige tallene fra A til F[kilde mangler], eller nævner blot tallene/bogstaverne i rækkefølge.

Nul

Et/En

To

Tre

Fire

Fem

Seks

Syv

Otte

Ni

Alfa

Beta

Gamma

Delta

Epsilon

Digamma

fx: Betaogtyve (Hex 2B/Decimal 43)

to-og-en-halv (Hex 2,8/Decimal 2,5)

For tocifrede tal kan vi udvide det klassiske "halvtreds(indstyvende) = 50", "firs(indstyvende) = 80" og få

Ti, Tyve, Tredive, Fyrre, Halvtreds, Tres, Halvfjerds, Firs, Halvfems, Fems(enstyvende), Halvseks(enstyvende), seks(enstyvende), halvsyvs(enstyvende), syvs(enstyvende) og halvotte(nstyvende).

Fx: digamma-og-halvottenstyvende (Hex FF/Decimal 255)

hundrede-gamma-og-fems (Hex 1AC/Decimal 428)

delta-hundrede-alpha-og-halvsyvs (Hex DDA/Decimal 3546)

epsilon-og-halvsyvs millioner, alpha-hundrede beta-og-halvsyvs-tusinde, epsilon-hundrede digamma og syvs (Hex DE.ADB.EEF/Decimal 3.735.928.559)

Kodning i spil

I mange spil, til f.eks. spilsystemet Nintendo DS, kan der, ved hjælp af kode-modulet Action Replay DS, opnås en række snydekoder, som bruger netop det hexadecimale talsystem. Her kan en hvilken som helst ting (f.eks. et våben eller et møbel), have sit eget hex(adecimal)nummer, som, hvis de andre dele af koden er sat rigtigt sammen, giver dig netop den valgte ting.

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