Computing - From Abacus to Transistors, the history

Bharat Kalluri / 2020-11-18

Computation or performing operations on numbers big and small is one of the fundamental necessities for humans. There are two basic operations, addition and subtraction. Everything else is built on top of these two basic operations.

Multiplication is just repeated addition. 5 multiplied by 2 is the same as 5 + 5.

Division is just repeated subtraction. 12 / 5 is just subtracting 5 from 12 repeatedly until we cannot subtract and then seeing what is the reminder. Since, 12 - 5 - 5 = 2. 12 goes into 5 two times with a reminder of 2.

Adding two numbers is one of the most important and basic arithmetic operations. Humans have an intuition for this to some extent. If we see 3 apples and 2 apples, we can count and say there are 5 apples in total (assuming counting is known). But once the numbers get bigger it will get harder and harder. One of the foremost efforts was abacus.

Iteration One: Abacus

Abacus uses beads and has levels. Each level will have a finite amount of beads. The lowest string of beads stands for units position, the second string stands for tens, third for hundreds etc..

If we had to add 13 + 11 , we first set up 13 in the abacus. By pulling 3 beads in the lowest string and 1 bead in the second level and then set up 11, by pulling one more bead in the first level and pulling one bead in the second level. Now if you read the abacus, you can see the answer! 24. Obviously there is a lot more to the abacus and it is a lot more capable, but you get the idea.

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There are problems to this, one is that people need to know how to use the abacus and the second is that it is still slow. Faster than computing by hand but not fast enough. We can do better.

Iteration Two: Stepped Reckoner

Lets jump in time to 1694, Gottfried Wilhelm Leibniz wanted to make computation easier and better. So he invented something called a stepped reckoner. A stepped reckoner uses cogs and gears to compute. It is a mechanical calculator. It does addition and subtraction, and for multiplication it just does repeated addition and for division it does repeated subtraction. Explaining how it works is really hard in text. So here are some videos explaining how it works.

Video explaining how a mechanical calculator should be used Video explaining how the internals work

This is great, but then there are issues with this approach as well. One is that sometimes calculations needed multiple steps, which was hard to accomplish using the step reckoner. Also the machines were heavy and expensive. Not everyone could afford a giant metallic mechanical calculator. And since it was fully mechanical, maintenance and repair was hard and expensive. We can do better! So we started caching!

Iteration Three: Pre computed tables

Mechanical calculators were great, but not everyone can afford it. So if you wanted a square root of a huge number, instead of getting a mechanical calculator. You could get a huge book which had all the basic, hard to calculate computations. Pre computed tables were especially useful for logarithmic and trigonometric functions.

A log pre computed table

You can find a lot more pre computed tables of the past here

These tables were heavily used during war time as they needed to calculate trajectories. Understanding trajectories was critical for armies to target and position artillery shells. The armies made extensive use of the pre computed tables. The army used a tables known as range tables which describe at what angle the machine should be fired based on atmospheric pressure, drift etc..

An example range table

These were extremely effective and were used until world war two. One of the problem was that if the cannon changed even by a slight bit, the whole book was to be recomputed. This was extremely time consuming and led to errors.

Iteration Four: The Difference engine

Charles Babbage understood that computing and calculating pre computed tables was very expensive and wanted to improve the system. So, he invented a machine called the difference engine. The difference engine was designed to tabulate polynomial functions. Polynomial functions are functions which come out with an output given a multiple variables. The trajectory calculation is a good example since the angle to position the cannon depends on the wind speed, the air pressure and many other variables.

Charles Babbage began constructing a proof of concept difference engine in 1819 and completed it in 1822. He announced his invention in 1822. In 1823 the British government gave Babbage £1700 to start working on the engine. The implementation proved to be very expensive and time consuming. In 1832 (That is 10 years later!) Babbage produced a small working model, which had one seventh of the promised capacity. Work stopped on 1833.

The difference engine

Meanwhile, Babbage started thinking about the next step. The Analytical Engine.

Iteration Five: The Analytical engine

This was probably the first general purpose computer. It could be used for more than one computation, can store and retrieve small amounts of data and even had a printer. But then Babbage could not get the machine working in practise even though he got the theory right.

But this was a mechanical system still, using punch cards as input. This will change soon as well.

Analytical engine

Iteration Six: Tabulating machines and International business machines

During 1890s, USA needed to do a census. But most of the census was done by hand and was extremely time consuming. So, The government turned to Herman Hollerith. Herman Hollerith invented a machine called a tabulating machine which takes in punch cards and adds and maintains census counts.

This helped the census system complete its work in around two and half years. It is estimated that, without the technology and just human effort. It would take around 12 years! Companies began recognizing the importance of computing in business and started extensively using machines for computing. From here after a couple of mergers a new company was formed for making these business machines and named itself International business machines or IBM for short.

But these machines were huge, heavy and not fast enough. One of the biggest business machine back then was Harvard Mark I. This machine was used by the infamous Manhattan project. This machine was huge, read through the wiki to understand more.

Harvard Mark One

The brains of the machine were relays. The relay has a control wire which generates a electro magnetic field, which in turn pulls the switch down thereby completing the circuit. If the control wire is off, then current does not flow. If the current flows, then some gear turns on and does some incrementing/counting etc.. The down side is that these relays are heavy and take time to move up and down. This means speed is a problem. Also since it is mechanical, it is subject to wear and tear. If a component stopped working in a giant machine, you can imagine how hard it would be to fix it and get it back to work. The Mark One almost had 3500 relays!

Iteration Seven: Vacuum Tubes

To increase speed and decrease wear and tear, we need ideally get rid of all moving parts. In 1906, Lee De forest invented exactly this, a vacuum tube. The idea is to have a two electrodes in a air tight glass bulb. And have another third electrode, which would be called a control wire. If the control wire was positively charged, it would allow current through.If it was negative or neutral, then current would not pass. So using a control wire, the circuit can be opened or closed.

If this sounds like a relay to you. You are right! This is essentially a relay. But without the moving parts. This is a huge step up since there is no moving parts. And they are fast, a relay can probably turn on and off around 30 times a second. A vacuum tube could turn on and off thousands of times per second!

Using vacuum tubes, the first fully electrical computer was made. Designed by Tommy flowers. The computer was called Colossus MK 1. It had a whopping 1700 vacuum tubes. It was used to decrypt nazi communications. Programming was done by plugging wires in plug boards.

But vacuum tubes were far from perfect. They were expensive, power hungry and would blow out like light bulbs. We needed something smaller and faster. In 1947, three scientists from bell labs made the next leap. Transistors.

Iteration Eight: Transistors

The physics is complicated. But the idea is that there is a gate electrode which is connected to two more electrodes. And when the gate has is positively charged. Then current flows through and the transistor switches on, else it switches off.

The earliest version of transistors were small and could switch between on and off around 10,000 times! This was a game changer and transformed how computers are made forever. Today, transistors power our processors, which are smaller than 50 nano meters!

Enough history, let us get to the meat of the subject.

Now that we can turn switches on and off super fast, how do we make use of this to do calculations? Enter logic gates.

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