We are accustomed to thinking in base 10. We use the numbers 0 through 9 to count. There are other bases we can use instead. We know the ancient Babylonians used base 60.
Binary (or Base Two) requires only two numbers, 0 and 1. Something this minor is the key to creating advanced technologies like computers and understanding neuroscience.
The base is a numerical system determines the range of numbers. Base 10 uses the number 0-9.
So in base 6, we use the number 0, 1, 2, 3, 4, and 5.
In base 6, 1+5 = 10. Why? There is no special symbol six, so 10 in base 6 = 6 in base 10.
We count in base 6 like this – 0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20 etc
So in numerical base 6 – 3+5 = 12. 3×5 = 23.
Using different bases for counting can have specific uses. Binary is the best for calculations. Radios and computers operate according to a binary system. The radio vacuum tube had two opearations – let voltage pass, or stay inactive. This requires a binary measuring system since there are only two possible symbols, 0 and 1. Computers operate the same way.
If you want to count to eleven in binary, you count using 1 and 0 so the number 11 in binary is 1011.
This is the how you get the answer: 1 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 = 11
So if you have 4 radio vacuum tubes, you activate tubes 1, 2, and 4, while leaving 3 inactive. This gives you 11.
You can count to much higher numbers in binary with a limited number of tubes and transistors than you could in decimals. Use your hands as an example. In Base 10, you can count to 10. With 10 fingers in binary, you can count to 1,023 (1111111111). That is 1 x 2^9 + 1 x 2^8 + 1 x 2^7 + 1 x 2^6 + 1 x 2^5 + 1 x 2^4 + 1 x 2^3 + 1 x 2^2 + 1 x 2^1 + 1.
This allows computers to do advanced calculations in seconds without using excessive numbers of transistors. Advanced mathematics that took decades by hand becomes possible through the use of binary calculating machines. Computers track vast amounts of numerical data and process it in seconds, allowing ever more advanced economic transactions and engineering projects.
What else thinks in binary? The human brain. Neurons function exactly like radio vacuum tubes and transistors. Nerve cells turn on and off. They allow an electrical pulse to pass through or they remain inactive. 1 and 0. The cumulation of 0s and 1s creates extraordinarily large numbers and calculations. The human brain has 10 trillion neurons and 10 quadrillion synapses.
That is a lot of calculating power.
Yet it seems like a lot of people don’t actually know what binary is, even if they have heard of it.