78 lines
3.1 KiB
Markdown
78 lines
3.1 KiB
Markdown
|
---
|
||
|
|
tags:
|
||
|
|
- binary
|
||
|
|
- computer-architecture
|
||
|
|
---
|
||
|
|
|
||
|
|
# 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:
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
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.
|