Here’s a standard joke involving representing numbers in different bases.

A: 57,005.

The joke, of course, is that $DEAD$ can be considered a number written in base 16, using the usual convention $A = 10$, $B = 11$, $C = 12$, $D = 13$, $E = 14$, and $F = 15$. In other words, $DEAD$ can be converted to decimal as follows:

$DEAD_{\small sixteen} = 13 \times 16^3 + 14 \times 16^2 + 10 \times 16 + 13 = 57,005$.

After I heard this joke, I wondered just how many English words can be formed using only the letters A, B, C, D, E, and F so that I could make a subtle joke on a test. To increase the length of my list, I also allowed words that included the letters O (close enough to a 0), I (close enough to 1), and/or S (close enough to 5). However, I eliminated words that start with O (since a numeral normally doesn’t start with 0) and/or end in S (the plural version of these words are easily formed).

So I wrote a small program to search the dictionary that I have on my computer. The unabridged list follows, with words beginning with a capital letter (such as names or places) listed at the bottom. I emphasize that this list is unabridged, as there are several words on this list that I wouldn’t place on a test for obvious reasons: I would never ask my class to convert the base-10 numeral 721,077 into hexadecimal just so they can obtain the answer of $B00B5$.

a

abaci

abase

abased

abbé

abed

abide

abided

abode

aboded

abscessed

abscissa

abscissae

acacia

accede

acceded

accessed

ace

aced

acid

acidic

acidified

aid

aide

aided

aside

assessed

b

baa

baaed

babe

babied

baobab

base

based

basic

bassi

basso

be

bed

bedded

bedside

bee

beef

beefed

beside

biased

biassed

bib

bid

bide

bided

boa

bob

bobbed

bode

boded

bodice

boo

boob

boobed

booed

bossed

c

cab

cabbed

cabbie

caboose

cacao

café

case

cased

cassia

cease

ceased

cede

ceded

cob

cobbed

cocci

cocoa

cod

coda

codded

code

coded

codified

coed

coffee

coif

coifed

coiffed

coo

cooed

d

dB

dab

dabbed

deaf

deb

debase

debased

decaf

decease

deceased

decide

decided

decode

decoded

deed

deeded

deface

defaced

defied

deice

deiced

deified

dice

diced

did

die

died

diocese

diode

disc

disco

discoed

disease

diseased

dissed

do

doc

dodo

doe

doff

doffed

dose

dosed

e

ease

eased

ebb

ebbed

eddied

edifice

edified

efface

effaced

f

fa

face

faced

fed

fee

feed

fiasco

fib

fibbed

fie

fief

fife

fob

fobbed

foci

foe

food

i

ice

iced

id

idea

if

sac

safe

said

sassed

scab

scabbed

scoff

scoffed

sea

seabed

seafood

seaside

secede

seceded

see

seed

seeded

sic

side

sided

so

sob

sobbed

sod

soda

sodded

sofa

A

Abbasid

Abe

Ac

Aida

Asia

Assisi

B

Ba

Basie

Be

Bede

Beebe

Bessie

Bi

Bib

Bic

Bob

Bobbi

Bobbie

Boccaccio

Boise

Bose

C

Ca

Case

Casio

Cassie

Cd

Cf

Ci

Cid

Co

Cobb

D

Dacca

Debbie

Dec

Decca

Dee

Defoe

Di

Dido

Doe

E

Eco

Ed

Edda

Eddie

Effie

Essie

F

Fe

Feb

Fed

Fido

I

Iaccoca

Ibo

Ida

Io

Isaac

Issac