eolas/zk/Why_computers_use_binary.md

---
title: Why computers use binary
categories:
  - Mathematics
  - Computer Architecture
tags: [binary]
---

# Why computers use binary

## Now we know how binary works, how does it relate to computing?

The reason is straight forward: it is the simplest way on the level of pure
engineering of representing numerical and logical values; both of which are the
basic foundations of programming. An electronic circuit or transistor only needs
to represent two states: on (1) and off (0) which corresponds to the switch on
an electrical circuit. A single circuit representing the binary values of 1 and
0:

![multi_on_off 1.gif](../../_img/multi_on_off.gif)

It would be much more complicated to have to represent ten different states
under the decimal number system, although denary computers do exist.

If we want more digits, we just need to add in more circuits, and we can
represent as large a binary number as we need. We just need one switch for every
digit we want to represent. The switches used in modern computers are so cheap
and so small that billions can be fitted on a single circuit board.

![multiple_circuits.gif](../../_img/multiple_circuits.gif)

When we use the term 'switch' we actually mean the transistor components of a
circuit. We don't need to know the physical details at this level but we can say
that a transistor turns a current on and off. They can also be used to amplify
the current.

On the level of electrical engineering and in the subsequent examples using a
light bulb and a simple circuit, the switch being OFF corresponds to the light
being ON, this is because the switch breaks the current. So when it is unbroken,
the current passes to the bulb. This also means that 1 corresponds to the switch
being OFF and 0 corresponds to the switch being ON which can be confusing at
first.

## From circuits to programs

The following breaks down how we get from the binary number system to electrical
circuits to computer programs:

1. ”Data”= a piece or pieces of **information**

1. In computing all data is represented in **binary form:**

   2.1. ”Binary” means that the value of a piece of data is exclusively one
   thing or another

   2.2. The values in binary code are exclusively 1 and 0 (either a piece of
   data is a 1 or it is a 0, it can never be both). Binary can also be expressed
   in logical terms where 1 is equal to `true` and 0 is equal to `false`

1. The smallest piece of data is a **bit**

1. We apply the binary number system to bits

1. Thus by 1-4, **a bit is either 1 or 0**

1. Binary form bears an isomorphic relation to switches on electrical circuits
   (the hardware of computers). Thus binary code can be _mapped onto circuits_.

   - Circuits are controlled by switches
   - A switch is a binary function: it is either on or off ”On/off”
     corresponding to 1/0.
   - In this way, switches control the flow of electric current

1. Thus by the above, hardware (which is a physical structure made up of
   electric circuits) is **readily programmable in binary terms**

1. Restatement of 6: in order for hardware to be programmed the program must
   provide the hardware with something that it can actually perform. The program
   must be formulated in binary code.