Come on, let's Add

Hi guys, let's look at early computing devices

Early Computing: Let's Add

Human Computers at NASA in the 1960s

In the early days, the word "COMPUTER" was used to describe the people who did calculations like addition, subtraction, multiplication and division with the help of an abacus, pen & paper, Napier's Bones etc. But, this was slow and error-prone and was also financially expensive.

  
As society grew more complex, the level and amount of computation also increased. Therefore, this approach was becoming inefficient, By the time of Industrial Revolution we were already building mechanical machines for tasks such as weaving, spinning, and manufacturing.

     
So why not build machines for these computations??

Blaise Pascal's Pascaline

So here comes the first practical gear-based mechanical calculator, the Pascaline invented by Blaise Pascal. He made it to help his father calculate taxes. It could only do addition & subtraction.

Stepped Reckoner

Later, Gottfried Wilhelm Leibniz improved upon Pascal's ideas by designing the Stepped Reckoner, which could perform multiplication and division. It used a special stepped drum mechanism for repeatedly adding a number which is the basic idea behind multiplication(Repeated Addition) and repeatedly subtracting a number which is division(Repeated Subtraction). 

So, what's the basic idea behind these gear-based machines?

Each position on the gear wheel represents a digit from 0 to 9, and each digit of the number has a corresponding gear.

So how is CARRY implemented,

Each gear corresponding to a digit has one extra-long tooth, so when we rotate it from 9 to 0 the long tooth engages with the adjacent digit's gear which rotates the adjacent gear by one position, hence incrementing it by one. This is how carry is implemented in those machines

So, how is subtraction done?

That's a topic for next time...

Want a hint??

hmm... what if we could transform subtraction into addition.