The digital computers you have on your desk

or in your pocket work on the basis of binary logic. This means that the information in

them is encoded in binary numbers which arenumbers that can take one out of two possible values; 0 or 1. The physical object that carries this binary information is called a bit. In everyday’s computers, the bit is represented by the state of a transistor inside a silicone chip. So for example, the 0 is represented by a low voltage on the transistor and the 1 is represented by a high voltage. You can think of the transistor as an electronic switch

that selects between two possible values of the voltage. Now, let’s say I have two bits. I can make four possible combinations of values – 0-0, 0-1, 1-0, 1-1 – which are the binary representations

of the four numbers from 0 to 3. If I have three bits, I can write from 0-0-0 to 1-1-1

which are all the numbers from 0 to 7. So with N bits, I can write the numbers from

0 to 2 to the power N minus 1. The way digital data is actually processed within a computer is by performing logic operations. The simplest one is on a single bit. It’s called the NOT operation and simply flips the value of the bit. 0 becomes 1 and 1 becomes 0. With two bits, I can do for example, the AND operation. This is the operation that returns 1 if both

inputs are 1. One can show that the negative AND gate, which is the AND gate followed by a NOT, is a universal logic gate. Any binary logic operation can be broken down into a sequence of NAND gates. Modern computers contain over a billion tiny silicone transistors connected in a way that allows a programmer to decide which sequence of logic operations takes place. They allow us to search the web, play games, prepare documents and perform

very complex calculations. But there are certain calculations that not even the most powerful super computer can tackle, such as finding the prime factors of large numbers, designing molecules and materials or finding the shortest path between many cities. For that, we need

a quantum computer.

## 7 Comments

## XORRE

hey wasn't this guy in a Numberphile video

## Crafted007

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## Marcel Pirosca

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## Ilic Sorrentino

Hey! there is a new series with prof Morello and you don't say on TV?!!!

## Krishna Chaitanya Manthripragada

I want to do my PHD now

## Ice Coffee

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