ALPHABETIC INTEGERS
Since the alphabet is often used for numbering (especially in lists), I always imagined it extended as an infinite number line, like numerals. Following the same principle as numbers, when all of the single digit characters are used up, then you move to a second digit, and the "ones" place repeats over. With the letters, since there is no "zero", and also to have an even numbered base, this system is modified from regular decimal-style notation. Instead of the base being "A0"; the first two digit integer, it is the last single digit integer, "Z". The next integer after that is "AA". If this was done with numerals, the number line would be [no zero] 1, 2, 3, 4, 5, 6, 7, 8, 9, 0(ten), 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 21, 22, 23…94, 95, 96, 97, 98, 99, 90(one hundred), 01(one hundred one), 02, 03, 04, 05, 06, 07, 08, 09, 00, 111, 112, 113…
So with the letters, it is basically a modified base 26, or icosaheximal system!
Most alphabetical numbering systems that have gone above "Z", often for some reason use only double digits: AA, BB, CC, DD…ZZ, AAA, BBB, etc. The most common place I have seen this is on court exhibits (which in supreme or civil courts are actually usually bound copies of documents). One 1991 Manhattan case went all the way up to "eeeee"! (which would have the numerical value of 108). But this wastes digits. In that system, the number of digits is the multiple of 26, with the numerical value of the digits being what is added to the multiple of 26. So EEEEE in this system would simply be DE! Spreadsheet programs like the one in Microsoft Works use this system, for the columns (while the rows are regular numbers), and since the entire grid has 256 by 256 fields, the rows run from 0 to 255; while the columns run from A to IV!
Just like decimal places are figured by adding powers of ten (the ones place being 1 (100)× the numerical value of the digit, + the tens place at 10¹ × the numerical value of the digit, + the hundreds place at 10² × the numerical value, and so on. So in this case, the "a’s" place is 1 (260) × the numerical value of the digit, and the AA’s place is 26 × its numerical value, and the AAA’s is 26² × its numerical value. AA is 26×1 (the value of A) + 1=27. BB is 2×26=54 + 2 = 56. AAA is 26²=676 + 26 +1= 703. Now, how about a bigger one? My name, ERIC is 5×26³ + 18×26² + 9×26, + 3 (87880+12168+234+3)=100285.
Here is the addition and multiplication table for all of the letters from A to Z:
ADDITION
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | + | |
| A | A\B |
C |
E |
A | |||||||||||||||||||||||
| B | B | D |
F |
B | |||||||||||||||||||||||
| C | C | F | I |
G |
H |
I |
J |
K |
L |
M |
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
C |
| D | H | L | P |
I |
J |
K |
L |
M |
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
D | |
| E | J | O | T | Y |
K |
L |
M |
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
E | |
| F | L | R | X | AD | AJ |
M |
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
AF |
F | |
| G | N | U | AB | AI | AP | AW |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
AF |
AG |
G | |
| H | P | X | AF | AN | AV | BD | BL |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
AF |
AG |
AH |
H | |
| I | R | AA | AJ | AS | BB | BK | BT | CC |
S |
T |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
AF |
AG |
AH |
AI |
I | |
| J | T | AD | AN | AX | BH | BR | CB | CL | CV |
U |
V |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
AF |
AG |
AH |
AI |
AJ |
J | |
| K | V | AG | AR | BC | BN | BY | CJ | CU | DF | DQ |
W |
X |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
AF |
AG |
AH |
AI |
AJ |
AK |
K | |
| L | W | AJ | AV | BH | BT | CF | CR | DD | DP | EB | EN |
Y |
Z |
AA |
AB |
AC |
AD |
AE |
AF |
AG |
AH |
AI |
AJ |
AK |
AL |
L | |
| M | Z | AM | AZ | BM | BZ | CM | CZ | DM | DZ | EM | EZ | FM |
AA |
AB |
AC |
AD |
AE |
AF |
AG |
AH |
AI |
AJ |
AK |
AL |
AM |
M | |
| N | AB | AP | BD | BR | CF | CT | DH | DV | EJ | EX | FL | FZ | GN |
AC |
AD |
AE |
AF |
AG |
AH |
AI |
AJ |
AK |
AL |
AM |
AN |
N | |
| O | AD | AS | BH | BW | CL | DA | DP | EE | ET | FI | FX | GM | HB | HQ |
AE |
AF |
AG |
AH |
AI |
AJ |
AK |
AL |
AM |
AN |
AO |
O | |
| P | AF | AV | BL | CB | CR | DH | DX | EN | FD | FT | GJ | GZ | HP | IF | IV |
AG |
AH |
AI |
AJ |
AK |
AL |
AM |
AN |
AO |
AP |
P | |
| Q | AH | AY | BP | CG | CX | DO | EF | EW | FN | GE | GV | HM | ID | IU | JL | KC |
AI |
AJ |
AK |
AL |
AM |
AN |
AO |
AP |
AQ |
Q | |
| R | AJ | BB | BT | CL | DD | DV | EN | FF | FX | GP | HH | HZ | IR | JJ | KB | KT | LL |
AK |
AL |
AM |
AN |
AO |
AP |
AQ |
AR |
R | |
| S | AL | BE | BX | CQ | DJ | EC | EV | FD | GH | HA | HT | IM | JF | JY | KR | LK | MD | MW |
AM |
AN |
AO |
AP |
AQ |
AR |
AS |
S | |
| T | AN | BH | CB | CV | DP | EJ | FD | FX | GR | HL | IF | IZ | JT | KN | LH | MB | MV | NP | OJ |
AO |
AP |
AQ |
AR |
AS |
AT |
T | |
| U | AP | BK | CF | DA | DV | EQ | FL | GG | HB | HW | IR | JM | KH | LC | LX | MS | NN | OI | PD | PY |
AQ |
AR |
AS |
AT |
AU |
U | |
| V | AR | BN | CJ | DF | EB | EX | FT | GP | HL | IH | JD | JZ | KV | LR | MN | NJ | OF | PB | PX | QT | QP |
AS |
AT |
AU |
AV |
V | |
| W | AT | BQ | CN | DK | EH | FE | GB | GY | HV | IS | JP | KM | LJ | MG | ND | OA | OX | PU | QR | RO | SL | TI |
AU |
AV |
AW |
W | |
| X | AV | BT | CR | DP | EN | FL | GJ | HH | IF | JD | KB | KZ | LX | MU | NT | OR | PP | QN | RL | SJ | TH | UF | VD |
AW |
AX |
X | |
| Y | AX | BW | CV | DU | ET | FS | GR | HQ | IP | JP | KN | LM | ML | NK | OJ | PI | QH | RG | SF | TE | UD | VC | WB | XA |
AY |
Y | |
| Z | AZ | BZ | CZ | DZ | EZ | FZ | GZ | HZ | IZ | JZ | KZ | LZ | MZ | NZ | OZ | PZ | QZ | RZ | SZ | TZ | UZ | VZ | WZ | XZ | YZ | Z | |
| × | 52 | 78 | 104 | 130 | 156 | 182 | 208 | 234 | 260 | 286 | 312 | 338 | 364 | 390 | 416 | 442 | 468 | 494 | 520 | 546 | 572 | 598 | 624 | 650 | 676 |
SQUARES: AJ=36, AW=49, BL=64, CC=81, CV=100, DQ=121, EN=144, FM=169, GN=196, HQ=225, IV=256, KC=289, LL=324, MW=361, OJ=400, PY=441, RP=484, TI=529, VD=576, XA=625, YZ=676 GR=200; KN=300; SF=500 WB=600; ZX=700; AGB=800; AHP=900 APH=1100; ATD=1200; Powers of 26: 26²=676; 26³=17576; 264=456976; 265=11881376; 266=308915776; 267=8031810176; AAA=703; AAAA=18279; AAAAA=475255; AAAAAA=12356631; AAAAAAA=321272407
BXX=2000; DKJ=3000; EWV=4000; GJH=5000; HVT=6000; JIF=7000; KUR=8000; MHD=9000
NTP=10000; VDX=15000; ACOF=20000
268=208,827,064,576; 269=5,429,503,678,976; 2610=141,167,095,653,376
Numerical values of two and three letter words
|
AD 30 AH 34 AL 38 AN 40 AS 45 AT 46 AW 49 BE 57 BY 77 DO 119 ED 134 EX 154 GO 197 HA 209 HE 213 ID 238 IF 240 IN 248 IS 253 IT 254 MA 339 ME 343 MY 363 NO 379 OF 396 OH 398 OJ 400 OK 401 ON 404 OR 408 OW 413 OZ 416 PA 417 SO 509 TO 535 UP 562 US 565 WE 603 |
ABE 733 ACE 759 ADD 784 AGE 803 AGO 873 AID 914 AIL 922 AIM 923 AIR 928 AKA 963 ALE 993 ALF 994 ALL 1000 ALM 1001 ALP 1004 ALT 1008 AMP 1030 AMY 1039 AND 1044 ANN 1054 ANT 1060 ANY 1065 APE 1097 ARC 1147 ARE 1149 ARK 1155 ARM 1157 ART 1164 ASK 1181 ASP 1186 ATE 1201 AWE 1279 AXE 1305 AYE 1331 BAD 1382 BAG 1385 BAM 1391 BAN 1392 BAR 1396 BAT 1398 BAY 1403 BED 1486 BEE 1487 BEG 1489 BEN 1496 BET 1502 BID 1590 BIG 1593 BIN 1600 BIT 1606 BIZ 1612 BOA 1743 BOB 1744 BOG 1749 BOP 1758 BOW 1765 BOX 1766 BOY 1767 BRA 1821 BRO 1835 BUB 1900 BUD 1902 BUG 1905 BUM 1911 BUN 1912 BUS 1917 BUT 1918 BYE 2007 |
CAB 2056 CAD 2058 CAN 2068 CAP 2070 CAR 2072 CAT 2074 COB 2420 COD 2422 COG 2425 CON 2432 COP 2434 COT 2438 COW 2441 COY 2443 CRY 2521 CUB 2576 CUE 2579 CUP 2590 CUT 2595 DAD 2734 DAM 2743 DAN 2744 DAY 2755 DEN 2848 DID 2942 DIE 2943 DIG 2945 DIM 2951 DIP 2954 DIS 2957 DNA 3069 DOC 3097 DOE 3099 DOG 3101 DON 3108 DOT 3114 DRY 3147 DUD 3154 DUE 3255 DUG 3257 DYE 3359 EAR 3424 EAT 3426 EBB 3434 EEL 3522 EGG 3569 EGO 3577 ELF 3698 ELK 3703 ELM 3705 ELY 3717 EMU 3739 END 3748 EON 3784 ERA 3837 ERR 3854 ESP 3890 EVE 3957 EWE 3983 EYE 4035 |
FAD 4086 FAN 4096 FAR 4100 FAT 4102 FAX 4106 FED 4190 FEE 4191 FEW 4209 FIB 4292 FIG 4297 FIN 4304 FIR 4308 FIT 4310 FIX 4314 FLU 4389 FLY 4393 FOE 4451 FOG 4453 FOR 4464 FOX 4470 FRY 4549 FUN 4616 FUR 4620 GAG 4765 GAP 4774 GAS 4777 GAY 4783 GEE 4867 GEL 4874 GEM 4875 GET 4882 GIN 4980 GNU 5117 GOD 5126 GOT 5142 GUM 5291 GUN 5292 GUT 5298 GYM 5395 HAD 5438 HAG 5441 HAL 5446 HAM 5447 HAS 5453 HAT 5454 HAY 5459 HEM 5551 HEN 5552 HER 5556 HEX 5562 HEY 5563 HID 5646 HIM 5655 HIS 5661 HIT 5662 HOG 5805 HOP 5814 HOT 5818 HOW 5821 HUB 5956 HUE 5954 HUG 5961 HUM 5967 HUT 5974 |
ICE 6167 ICY 6187 IKE 6375 INK 6459 ION 6488 IRA 6553 IRE 6557 IRK 6563 IVY 6681 JAB 6788 JAH 6794 JAM 6799 JAR 6804 JAW 6809 JAY 6811 JET 6910 JEW 6913 JIG 7001 JOB 7152 JOE 7155 JOG 7157 JOT 7170 JOY 7175 JUG 7313 KAY 7469 KEG 7573 KEN 7580 KEY 7591 KID 7674 KIM 7683 KIN 7684 KIT 7690 LAB 8140 LAD 8142 LAG 8145 LAP 8154 LAW 8161 LAX 8162 LAY 8163 LED 8246 LEG 8249 LEO 8257 LET 8262 LIB 8348 LID 8350 LIE 8351 LIP 8362 LIT 8366 LIZ 8372 LOB 8504 LOG 8509 LOP 8518 LOT 8522 LOW 8525 LUG 8665 LYE 8767 |
MAD 8818 MAN8828 MAP 8830 MAT 8834 MAX 8838 MAY 8839 MEN 8932 MET 8938 MID 9026 MIT 9042 MIX 9046 MOB 9180 MOM 9191 MOP 9194 MOW 9201 MUD 9338 MUG 9341 MUM 9357 NAB 9492 NAG 9499 NAP 9508 NAT 9512 NAY 9517 NED 9598 NET 9614 NEW 9617 NIP 9714 NOT 9874 NOW 9877 NUN 10024 NUT 10030 OAF 10172 OAK 10177 OAR 10184 OAT 10186 ODE 10249 OIL 10386 ONE 10509 ORB 10610 ORE 10613 OUR 10704 OUT 10706 OWE 10743 OWL 10750 PAD 10846 PAL 10858 PAN 10860 PAT 10866 PAW 10869 PAY 10871 PEG 10953 PEN 10960 PET 10966 PEW 10969 PIE 11055 PIG 11057 PIN 11064 PIT 11070 PLY 11153 POD 11210 POP 11222 POT 11226 POW 11229 POX 11230 PRO 11295 PRY 11305 PUB 11354 PUN 11376 PUP 11378 PUT 11382 |
RAD 12198 RAG 12201 RAM 12207 RAN 12208 RAP 12210 RAT 12214 RAW 12217 RAY 12219 RED 12302 REX 12322 RIB 12404 RID 12406 RIG 12409 RIM 12415 RIP 12418 ROB 12560 ROD 12562 RON 12572 ROT 12578 ROW 12581 ROY 12583 RUB 12716 RUG 12721 RUM 12727 RUN 12728 RUT 12734 RYE 12823 SAD 12874 SAG 12877 SAM 12883 SAP 12886 SAT 12890 SAW 12893 SAX 12894 SAY 12895 SET 12994 SEW 12997 SEX 12998 SHY 13077 SID 13082 SIN 13092 SIP 13094 SIS 13098 SIT 13098 SIX 13102 SKA 13131 SKI 13139 SKY 13155 SLY 13181 SOB 13236 SOG 13241 SON 13248 SOW 13257 SOY 13259 SPA 13261 SPY 13285 STY 13389 SUB 13392 SUD 13394 SUE 13395 SUM 13403 SUN 13404 |
TAB 13548 TAG 13553 TAN 13560 TAP 13562 TAR 13564 TAX 13570 TED 13654 TEN 13664 THE 13733 THY 13753 TIE 13759 TIM 13767 TIN 13768 TIP 13770 TOE 13915 TOM 13923 TON 13924 TOP 13926 TOT 13930 TOW 13933 TOY 13935 TRY 14013 TUB 14068 TUG 14071 TUT 14084 TWO 14133 UNO 14575 URN 14678 USE 14695 VAN 14912 VAT 14918 VEX 15026 VIP 15122 VIZ 15132 VOW 15285 WAG 15581 WAR 15592 WAX 15598 WAY 15597 WEB 15680 WED 15682 WEE 15683 WET 15698 WHO 15771 WHY 15781 WIG 15789 WIN 15796 WIT 15802 WIZ 15808 WOE 15943 WOK 15949 WON 15952 WOW 15961 WRY 16041 YAK 16937 YAM 16939 YAY 16951 YEA 17031 YEN 17044 YES 17049 YUM 17457 ZAP 17618 ZEN 17720 ZIP 17826 ZOO 17981 |