Grace Brewster Hopper

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At present, the multiplication time for the computer is 3 milliseconds, and the sddition time is 80 microseconds. These present times are partly due to safety factor delays which have been built into the arithmetic control circuitry

by means of mono-stable fllp-flops. Wlth the present arithmetic control, a multiplication time of 1 millisecond and an addition tlme of 50 microseconds seems feasible.

M A C H I N E AIDS TO C O D I N G By

Naval Research Coding process

of

for

A problem

be expressed

of several forms of tation

types logical

the

volving variables, direct

code of

the

to be computed

result

language.

out

difficulty.

arranged

in

In these

cases

checking

often

clerical

errors.

and the

fails

set

translation

from one structure

translation

of words,

a relatively ample,

consider

for

Let

the the

for

is

for

to

done. is

cated

that

the

complex and

substitution

algebraic

of

symbols.

expression

Is

addition

this

Assume the

use 17

necessary ~rocess, auxiliary

symbol

for

multiplication

add2.

The

then 2 i 2 I

this

codes,

algebraic

M.

fact

003 004 005

machine

OOl 002 004 003 step

005 005 005 005 is

merely

symbols

Nevertheless,

inevitable,

multiplication,

in-

correspondence

ment of equivalent

one

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for

is

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process.

symbol

is

the

the

1 and for

004 005 005 005

pass-

another,

the

translation

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substituting

symbols

simple

y=ax2~bx~c. b e A,

convention

the

grammar of

is

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of

grammar,

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u s make t h e

ition

translation

separate

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can be divided

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is

step

symbols

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four

y ~

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unique.

most extensive

of words.

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machine

y y

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process

grammar and translation the

not

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paths.

grammar would

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in general

and

the

expresses

to eliminate

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that

machine.

many i n s t r u c t -

translation

of

y = a x 2 ~ b x 4~ c i n

and checked

complex alternative

becomes formidable

structions

reasonably

few variables

the

a sequence

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in-

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a great

with

xia yA b y Mx y A c

o f many

and can be written

of

be:

no-

those

address

location.

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is

dealing

then

a three

form operator-order-operand-

must be translat-

processing

require

requires

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notation

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translation

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roughly

from one language

particularly

the

little

ions

design

symbolism.

iteratfve

a

in one of several

machine

many problems,

with

or

is

machine

in algebraic

or symbolism

ed Into

computers

translating

¢o a n o t h e r . Bight

digital

E a r l Y. I s a a c Laboratory, Washington

in

clerical

it

long

errors

a replaceis

and compliare

and long and arduous to avoid

them.

easily

almost checking

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an obvious

recourse

machines.

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the

is coder

to

wrote

in machine

grammar hut

arbitrary

symbols

for

auxiliary

equipment

the

words,

could

midges..~MD

used the

perform

the then

substitution. The use in

coding

of

an arbitrary

instead

specific

of

machine

principle

locations

has

first

is

arbitrary

symbolism

permits

redundant

dictionary;

the

major

rearrangements

without

altering

possible. the

of

permits

as

the

the

cues

out

recourse

coder

to

to

so

the

that

the

lS

in

to

particularly

when the

relationship

to

example, follows

i.e.,

serve re-

symbolism

specify

have

fleas

N

ions

are

made

locations

to

maintain

experience.

For

a dictionary

code

the

auxiliary

1

are

2

National

~

4

dictionary

have

~

5

the

midge8

have

germs,

midges."

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this

symbolism

almost

constant

reference

ary

to

translate.

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the

dictionary

instead,

the

or

are

then

ion

is

ing

run

on an

the

we s p e c i f y

structure

a code

~

DO

operations

fleas

~

FL

as 18

convenient

reproducer

for

the

SEAC.

into

one

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deck

themselves, machine

and

together addresses,

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interspersed

gang

punch-

IBM r e p r o d u c e r . above

appears

of

no

a redundant

together.

the

to

translation

in the as

terms

of

particular any other

of

be considerably

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directly

dogs

with

another.

more difficult.

:

and

Standards

words

made by an

has

by elementary

punched

sorted

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be done with

codes

written

into

order

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translate

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diction-

can

of

in

coding.

corresponding

punched

but

IBM s o r t e r

are

are

requires

to

coding

relative

correct-

a reassignment

arrangement.

dictionary the

or

block

Bureau

germs

translates

code,

type

separated

the

an

instructions

and

necessary

itself

to

same

changes

equipment.

used

the

purposes.

often

the

midges ~, 3

fleas,

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a machine on

of

the

freedom

arrangement

together

in

is

is

computer

with

have

grouped

instructions.

it.

checking

variables

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1 5 2 3 5 4 2 5 3

fleas

example,

which

construct-

advantage

for

to

readily

while

A block

For

no

write

"Dogs have

both

main

By u s i n g

can

checking

many advantages

with-

quantity

coder

code

has

of

the

the

from

translated

dictionary.

rearrangement.

application ~

the

and while

be

be

suggest

his

effect

: dogs

which

to

that

disrupts

no re-

symbols

it

should

understand,

previous

we c a n

of

standpoint,

with

easily

The second

are

they

machine

language

difficult

ing

that

necessary,

quantity

HV

correspond

locations

symbols

from an engineering

dundancy

is

can

interpret

a

mnemonic symbols

physical

an arbitrary

of

coding

than

is

costly

use

dictionary,

use

they

the

second

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then

two

the

present.

as

phrase

specific

more symbols

variables,

but

the

that

relative

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use

for

of

~

to

symbols

advantage

have

DO HV FL MD HY GR FL HY MD

advantages.

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~GR

write

symbolism

reference

germs

the

that

writing

allowed

machine form.

is

The use

of s u b r o u t i n e s

the

permits the coder to think

positions

occupied

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the

c o m b i n a t i o n s of the e l e m e n t a r y a r i t h m e t i c

punches

control

and logical o p e r a t i o n s

reproducer

in terms of functions

that are c o m p l e x

of the machine.

that

This is in effect a different s t r u c t u r e

that

than that p e r m i t t e d by the basic machine.

appropriate

The t r a n s l a t i o n p r o b l e m in this case

deck.

the r e p l a c e m e n t for

the

system

in is

the

by t h e

machine

now u n d e r

Naval Research

development

Laboratory

to

a single-address

the

For

purely

system

will

permit

the

coder

in each

instruction,

written

dundant

dictionary,

up to six

for

a subroutine,

routine,

where

to store

the

subroutine

and an arbitrary

control

if

necessary.

process

uses

producer

only

in

of

the

(2)

translation

of

the words.

structions the

the is

number of

routine

is

counted.

cards

are

These

contain

of

the

dundant

occurrences

prepared the

subroutines

r o u t i n e cards.

Standard for

each

complete with

form and with

sub-

completed

the

the

previously.

left

This

deck while

in

the

the in-

information cards

the read feed

then transfer

the

the

positions on the subWhen a subroutine

next

instruction

dundant d i c t i o n a r y .

in-

is

card i s

in terms

of the com-

translatlon

The second is

The computer

and sub-

form the

processes

of

a careful

analysis

or

subroutine.

blanks

decks

in

puter but with symbols still from a re-

word

constants

placed

the first card

of the e l e m e n t a r y o p e r a t i o n s

In the

coded

is

c o n t a i n i n g a set of i n s t r u c t i o n s

and

sets

subroutine

This process results in a deck

read.

of

and re-

of each

the

from the g a n g - p u n c h e d columns

of

by s u b r o u t i n e s

into

deck.

Selectors

into a p p r o p r i a t e

structure,

deck containing sorted

symbols

a re-

two s t e p s :

translation

step

is held.

transfer

(1)

first

to specify

of

the

selectors

the

deck

of

is g a n g - p u n c h e d hack into s u c c e s s i v e

The translation

place

is p u n c h e d

of the s u b r o u t i n e

results

of

subroutine

of the s u b r o u t i n e

this

the

feed

into

in

contain

As each instruction card

arguments

a n IBM s o r t e r

and takes

the

operations

using

designation

arguments

feed,

formation

the

computer,

arithmetic

read

decks

read

timing

The instruction

arguments.

passes under the r e a d i n g brushes

A

perform

for

this

at

the

positions

punch feed.

equivalent

terminology.

translation NAREC.

the

of the coder's e x p r e s s i o n

complex operation

structure

is

subroutine

and the

punch the

by t h e

not

itself

any advantage

using

the

in re-

stead

of

for

use.

pattern

computer the

performed

step

as

described

can obviously

described

above.

can determine

elementary

this

whether

purpose

machinery

perOnly

would be gained for

of

by in-

now i n

COMPUTER AIDS TO CODE CHECKING By I r a C. D i e h m N a t i o n a l B u r e a u of S t a n d a r d s , W a s h i n g t o n W h e n a complex r o u t i n e is t r i e d on a c o m p u t e r for the first time, it is seldom f o u n d to be free from error. The t r e n d t o w a r d a u t o m a t i c p e r f o r m a n c e of the c l e r i c a l p a r t s of the coding p r o c e s s should r e d u c e the n u m b e r of coding errors. This m e c h a n i z a t i o n of c o d i n g is the subject of several

p a p e r s at this conference. Nevertheless, a significant a m o u n t of v a l u a b l e c o m p u t e r time w i l l c o n t i n u e to be d e v o t e d to the search for oodlng e~cors. Careful proofreading and clerical c h e c k i n g are o b v i o u s but important 19