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, 2394, 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, DDZZ, 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 10 the numerical value of the digit, + the hundreds place at 10 the numerical value, and so on. So in this case, the "as" place is 1 (260) the numerical value of the digit, and the AAs place is 26 its numerical value, and the AAAs is 26 its numerical value. AA is 261 (the value of A) + 1=27. BB is 226=54 + 2 = 56. AAA is 26=676 + 26 +1= 703. Now, how about a bigger one? My name, ERIC is 526 + 1826 + 926, + 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  

MULTIPLICATION

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;
BXX=2000; DKJ=3000; EWV=4000; GJH=5000; HVT=6000; JIF=7000; KUR=8000; MHD=9000
NTP=10000; VDX=15000; ACOF=20000

Powers of 26: 26=676; 26=17576; 264=456976; 265=11881376; 266=308915776; 267=8031810176;
268=208,827,064,576; 269=5,429,503,678,976; 2610=141,167,095,653,376

AAA=703; AAAA=18279; AAAAA=475255; AAAAAA=12356631; AAAAAAA=321272407
 

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

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