Saturday, 1 July 2017

The Inventor of Binary: Willhelm Gottfried Leibniz




Willhelm Gottfried Leibniz invented binary, the number system at the heart of modern computers. Leibniz biscuits were also named after him.

Leibniz was born on July 1st 1646. He was a German mathematician and philosopher. Leibniz was a contemporary of Sir Isaac Newton and both independently developed calculus.

Leibniz published a paper on binary in 1703 explaining his ideas. He first wrote about binary in 1679.

Leibniz, Like the Biscuit?

A lot of children will be more familiar with Leibniz biscuits than the German mathematician. But is there any connection? I had always assumed it was a coincidence. But no, the biscuits are named after the man. 

According to the Bahlsen website: "[Gottfried Wilhelm Leibniz] spent the last forty years of his life in Hannover, in the employment of the local nobility. This combination of local residency and wide-ranging thinking struck a chord with Hermann Bahlsen, who named the biscuit in his honour."

Well, that's rather awesome. So now I have a new way of teaching binary to kids. Choco Leibniz biscuits. Flip them chocolate side up for a one and chocolate side down for a zero!

What is Binary?

Binary is a system of counting that uses base 2 instead of base 10. The rightmost digit has a value of 1 and each digit to the left doubles. So instead of 1, 10, 100, 1000, 10000 as in decimal numbers, the place are worth 1, 2, 4, 8, 16, 32, etc - the powers of 2. 

For example: In binary 10 is 1010 which is an 8 plus a 2.



There are 10 types of people: those who understand binary and those who don't. 
The joke "There are 10 types of people: those who understand binary and those who don't." works because, in binary, 10 represents the number two. 

At first this might seem inconvenient, binary numbers are much longer than their decimal equivalents. But the reason they are so important in computing is that electronic devices can detect two states - on and off, or 1 and 0. You can read and write binary numbers when you have a way of telling the difference between two states.

Learning Binary with Leibniz Biscuits

You get 9 biscuits in a pack of Choco Leibniz. We recommend starting with 3 or 4 biscuits and working up to 8. We're sure you can think of something to do with the 9th biscuit. 

Start with all the biscuits chocolate side down. This represents the number 0. Every digit is zero. Helpfully the biscuits even look like digital 0's from the back!


If you have four biscuits then they represent 8, 4, 2 and 1 and you can count from 0 to 15 (8+4+2+1.) 


Flip a biscuit over to turn a digit into a one. This is the number 1 in biscuit binary:


This is 10 in binary (8 + 2):


Here's a quick video of counting in 3 bit biscuit binary:




Why not make it a family tradition to recap binary every time you have a packet of Leibniz biscuits.

If you want to make really big binary numbers then we recommend choosing Bahlsen Choco Leibniz Mini biscuits.

In binary, each place or digit is called a 'bit'. With 16 biscuits you can represent the numbers from 0 to 65535.

Binary and the I-Ching

Leibniz was aware of the hexagrams in the I-Ching. He was interested in philosophy as well as mathematics.

The I-Ching is an ancient Chinese system for trying to predict the future. The I-Ching has 64 symbols (yep, that's a power of 2) represented with 6 lines where each line is either solid or unbroken (2 states.) The states correspond to the notion of Yin and Yang (dark and light, or chocolate and plain.)



Leibniz mapped the I-Ching symbols to binary and was impressed that the ancient Chinese had invented the system. 

Should Kids Learn Binary?

Do children need to learn binary? Actually you rarely need to use binary to work with a modern computer, all that stuff is pretty well hidden. 

But we think it's important that kids understand how technology works to demystify it. We also think it's important that children understand the history of technology and the inventions that have made it possible. Binary is a big one!

The First Computers to Use Binary

Leibniz actually realised that binary could be used for automated calculation. "[Leibniz] imagined a mechanical calculator, in which marbles could fall through an open hole to represent one and remain at a closed hole to represent nought." source He didn't build this machine though he did build other calculating machines. 

German inventor Konrad Zuse worked on the Z1 an early electro-mechanical computer that used binary in the mid 1930s. 

At first Zuse's work wasn't known about outside Germany and the development of computing progressed in parallel elsewhere. 

George Stibitz came up with the idea for the first digital computer which used binary. In 1937 he built his binary adder using relays. You can watch him explaining his idea in this video:



Thanks Leibniz

Who knows where modern technology would be without Leibniz's formalisation of binary numbers. We wonder what he would have made of the significance of binary in the modern world. And of teaching binary with chocolate covered biscuits named after him.



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