From: Vagabondo <vagabond@cruzio.com>
To: Ray McKay
Date: Fri 11/7/2003 5:33 PM
Subject: Interesting information on Comptometer Model H

Brooke

From: Ray Mackay <raymondmackay05@optushome.com.au>
To: Vagabondo
Date: Fri 11/7/2003 3:42 PM
Subject: Interesting information on Comptometer Model H

Ray

From: Ray Girvan <ray@RAYGIRVAN.CO.UK>
To: CALCLIST
Date: Fri 11/7/2003 3:20 AM
Subject: Comptometer: Division (C. Nöring)

Ray Girvan

From: Gilbert Harrus <Gilbert.Harrus@xrce.xerox.com>
To: Ray McKay
Date: Fri 11/7/2003 12:14 AM
Subject: Division on a Comptometer 

Gilbert

From: Nicholas Bodley <nbodley@WORLD.STD.COM>
To: CALCLIST
Date: Thu 11/6/2003 6:19 PM
Subject: Comptometer: Division (C. Nöring)

Nicholas Bodley
Waltham, Mass.

From: Ray Mackay <raymondmackay05@optushome.com.au>
To: James Redin
Date: Thu 11/6/2003 4:02 PM
Subject: Division on a Comptometer

Ray

From: Derek Peschel <dpeschel@ESKIMO.COM>
To: CALCLIST
Date: Thu 11/6/2003 2:18 PM
Subject: Division algorithm for Comptometer (and similar machines)

With ordinary subtraction you pad your number at the left with 9s (on the Burroughs key-driven machines) or use one of the carry cut-offs (on the Comptometer). With division you intentionally do not pad the number, so that the carries will build up in the next column over which holds the current quotient digit.

-- Derek

From: Christofer Nöring <christofer.n@TELIA.COM>
To: CALCLIST
Date: Thu 11/6/2003 7:55 AM
Subject: Division Algorithm

Christofer Noering
Stockholm

From: Ray Girvan <ray@RAYGIRVAN.CO.UK>
To: CALCLIST
Date: Thu 11/6/2003 7:06 AM
Subject: Division Algorithm

Ray Girvan

From: Ronald A. Kriss <rkriss@gunster.com>
To: james@dotpoint.com <james@dotpoint.com>
Date: Thursday, August 19, 1999 8:08 AM
Subject: Burroughs Calculator


Just got a Burroughs Calculator, 9 rows and 9 columns with an extra 9 in the upper left hand corner.  Serial no. 5-476631.  Says Burroughs Calculator on front and Burroughs on the back.

What are the little numbers for?
And what are the little knurled knobs at the bottom near the back for?
Can you use the machine to subtract?
Do you know about how old it is?
What are they worth?  (I paid $16 in a store in Massachusetts - I would have paid MUCH more!)

Hope you can help with these answers.

Ron Kriss

What are the little numbers for?

I'll jump in, here, at the risk of putting out wrong information.

I'd make a semi-educated guess that this is a Comptometer (TM, Felt and Tarrant)-like mechanism that can internally add, only, but when you add the complement of numbers, it effectively subtracts. The Curtas use complementary subtraction. (Set all slides to zero, and  pull out the crank. Turn once. Watch all accumulator dials make exactly one turn. Good test of the carry mechanism.)

If the little numbers, added to the big ones, add up to 9 (10?), then this must be the case.

Let's say,

5 - 3 = 2

Take the tens complement of 3, which is seven. Add 5 and 7 to get 2, but with a carry out the high end.

87 - 34 = 53

Now, you'll see that you need a tens complement in the least-signif. digit (units) position, but the nines complement in the others. (Curtas do this.)

Units, first:

Tens complement of 4 is 6, so add 7 and 6 to get 3 and a carry. Nines complement of 3 is 6, so add 6 and 8 to get 4 with a carry out the high end, then add in the carry from the units digit to get 5.

You should get a bell or some indication that there was a carry out the high end, if the result has a positive sign.

It's basic, but I don't recall how you'd subtract a small number; you probably have to enter (nines complements of zero) in all higher-order columns.

Afaik, Comptometer operators would have entered a 4 and then a 5 into those higher-order columns.

1) Hope this helps
2) Hope I didn't make any silly goofs. (Mailing-list addict, here!)

|*  Nicholas Bodley    *|*  Autodidact & Polymath * Electronic Tech. (ret.)
|*   Waltham, Mass.   *|*   -----------------------------------------------
|* nbodley@WORLD.STD.COM  *|*   Before 1960 or so: $100. Later: 100$
|*  Amateur musician  *|*  Before 1990 or so: 100%. Later: %100
--------------------------------------------------------------------------

The nines complement technique can be used to subtract on any machine that can add.  Suppose for convenience that we have a 4 digit adder, and that we want to compute x-y.  We can write x-y as

  x-y = x + (9999-y) + 1

Note that 9999+1=10000, and the 10000 simply carries off of the end of our four digit adder.

Computing 9999-y is easy- just replace each 0 in y with a 9, each 1 with an 8, each 2 with a 7, and so on.  Adding x+(9999-y) is easily done with the four digit adder.   Adding an extra 1 at the end is also easy.

For example, suppose we want to compute 7853-5678

The 9's complement of 5678 is 4321.  So we add

           7853
          +4321
          +     1
          --------
           2175

Because we've got a four digit adder, the left most 1 never appears.

I've seen a number of calculators (Such as the Hoffritz and Swift Handy Calculator)   that have the 9's complement digits labeled on the calculator.

Note that if you want to subtract a relatively small number, you'll have to include all of the leading 9's to get a correct answer.

You can also use this scheme to represent negative numbers.  -y is represented as 10000-y for y between 1 and 5000.  In this system, any number that begins with the digits 0-4 is positive, while any number that begins with the digits 5-9 is negative.   For example,

  number                     is represented as
  -1                              9999
  -4000                         6000
  -5000                         5000

Note that the range of representable negative numbers is -5000 to -1, while the nonnegative numbers range from 0 to 4999.

Some terminology:  The number (9999-y) is called the 9's complement of y.  The number (9999-y)+1 is called the 10's complement of y.

It's interesting that this same technique is used in binary form in modern digital computers.  In that case, you use the ones complement (all ones replace by zeros and vice versa)  for subtraction, and negative numbers are written in twos complement form.

Brian Borchers                              borchers@nmt.edu
Department of Mathematics          http://www.nmt.edu/~borchers/
New Mexico Tech                          Phone: 505-835-5813
Socorro, NM 87801                        FAX: 505-835-5366

(Somewhat off-topic:)
(Background:)

As a bit of a follow-up to Brian's nice exposition, it might be of interest to note that "business" computers, back in the earlier days, used several bits to represent each decimal digit; they were decimal-oriented, although binary in detail. Sometimes this was called BCD, or binary-coded decimal. (IIrc, IBM had to be different, and called it DCB.)

Converting to natural binary on input, and converting back to decimal on output came later.

=====

What prompted this message was that some ways of defining the ten digits in binary were cleverly planned so that reversing every bit created the code for the nines complement.   One was called excess-three, or "XS3", perhaps. Using 8-4-2-1 weighting, the binary number was three greater than the digit. 0 was 0011, 1 was 0100, etc. There were others; iirc, 2-4-2'-1 was another; no combination of bits could represent a digit greater than 9.

Hi Ron: I picked up one of these machines within the last year and paid about what you did, perhaps a few dollars less. I thought it was a bargain. I believe it is a class 5 calculator, ca. 1927. I'm not an expert on these, but it may function like a Comptometer, and I would almost be sure that it can subtract, but I haven't put it through its paces.

The little knurled knobs are unscrewed to help remove the top cover. Others on the Calc List know more than I do about this machine, but this is a starter.

Frank Lindauer

Although I did not receive Ron's enquiry regarding Burroughs' and therefore do not know of which model or system he speaks I feel I should stick my bib in.

Firstly 'Key Driven machines' of the Comptometer type consisting of a number of columns of nine keys were completely capable of Multiplication and Division plus extracting a square root.

They were work to apportion amount and calculate percentages and mark-ups. AFAIK any machines of this type and any machines capable of additon and subtraction are fully capable of Multiplication and Division as these functions are merely repeated addition and subtraction moving to the next higher or lower order as dictated by the result.

Models were constructed that work in Decimal, Sterling, Weights and Measures plus other specialised numbering systems.

Other adding machines with a ten (or more) numeral keypad and a series of function keys entered data into a pin box or other type of register from where it performed additions or other function via repeated addition and subtraction.  Some wrere more sophisticated than others and to speed up a process were capable of 'flagging' if a number was higher or lower than five and changed the method of calculation accordingly.  Thus reducing the number of repetitive cycles.

Burroughs' made machines of several types, the parallel to the Comptometer introduced to the market close to or maybe even before the time the Comptometer was released,  A largish listing machine with glass side panels and a side actuating lever (I recall some of these had print  outs, but memories grow weak with the years) plus other developments. They produced both mechanical and electronic machines.

James Redin's site contains mechanical details of some of these machines. Vagabond's site further details.

If any one wished to ask specifica question I will answer to the best of my ability to recall.  Messages to this site are restricted in site so I can not ramble on and get the message through

Divisions on adding machines.

Some machines had cut offs called subtraction cut offs these precluded the requirement of entering all the nines to the left of the calculation.  All this mechanism did was lose the carry. 

It should be noted that in Division on 'Key Driven' machines the negative carry was most important as it made its own specific noise as the carries ran across the machine. This told the skilled operator to add back the divisor and move her figures one position to the right before starting to subtract once again.

This process was repeated across the machine until the right hand columns were reached.  Its interesting to note that some models of Burroughs' actual had a single nine key in the left hand column specifically for running nines across the register.

The Burrough's 'Key Driven' Comptometer type machine did all the functions of the Comptometer. This included Addition, Subtraction, Multiplication and Division plus the extraction of square roots.

The keydrive mechanism was totally different from that used in the Comptometer as also was the Carry Over Mechanism.  The carry over mechanism being located inside the numeral wheel. As the number increased to the left of a wheel two small pinion rotated inside the next wheel to the right.  When the lower order wheel reached 10 it triggered the pinion mechanism rotating the 'skin' or outer numeral wheel to add in the one.  It was very fast and afaik was not subject to errors caused by duplication of carries ie

The actual keydriven mechanism was the typical parallel bars being pushed down and operating a segment which engaged the register pinions. Although I worked on them from time to time I did not convert them to decimal currency.  Basically this means the full adjustment process was never embedded in my mind. Walthers and Comptometers I know from A to Z

multiplying 334 continuously  or 375 continuously.  These tests were mandatory before machines were sent out to clients and once machines performed these calculations through all keyboard position many time they were considered suitable to send out to the client.

regards Ray Mackay