Switches
Building a generic machine
What could we base it on?
What fundamental component do we need
Modern digital computers are based on electronic switches
These electronic switches areStarting with something very simple, we can combine it into something much more capable
Starting with a switch you can control a light:
What if you connect multiple switches? Then all of them must be on for the light to be on:
This would be good for example if you launch a rocket and you want the checklist to be followed:
rocket
NAV GO COM GO LAUNCH |
battery - switch - switch - switch - ignitionIf we combine switches in a different way, then only one OR the other needs to be on:
What else could we do? We could try making a calculator that can add numbers more accurately than we can
Unfortunately it seems like we’re going to need a lot of switches and lights just to add two single digit numbers:
0 1 1
battery - switch - switch - light
0 2 2
battery - switch - switch - light
...
1 9 10
battery - switch - switch - light
...
2 8 10
battery - switch - switch - lightImagine if we want to add even larger numbers!
How can this be fixed?
Two steps:
First, one issue we were running into was that there are ten values for a single digit number:
0 1 2 3 4 5 6 7 8 9This means when adding two single-digit numbers, there are a lot combinations (10 * 10 = 55)
What if instead we reduced the number of digits?
What if we reduced to only 0 and 1 digits and stopped using the other digits, then we’d have to deal with only 4 combinations
let’s focus on 0 and 1:
0 0 0
battery - switch - switch - light
0 1 0
battery - switch - switch - light
1 0 1
battery - switch - switch - light
1 1 ?
battery - switch - switch - lightHere’s a problem, with 1 and 1 - we know the answer is 2 but we’re not using any digit other than 0 or 1, so what do we do?
Well with regular decimal digits, imagine a counter incrementing:
000
001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021You can see that after 009, we change the next 0 -> 1, and 9 -> 0, then after 019 we change 1 -> 2, 9 -> 0. In other words we reset the last digit to 0 and increment the next place. Similarly once we get to 099, we get 100. This time we reset two 9s.
So in a similar way what if we’re only using 0 and 1, then we get the following
000 (0)
001 (1)
010 (2)
011 (3)
100 (4)
101 (5)
110 (6)
111 (7)So after 001, we change the next 0 to 1 and reset the 1 to 0.
This is known as binary (bi -> 2) which is a different notation than regular decimal (dec -> 10)
And we have the answer to our question of 1 and 1 - it’s 10!
0 0 0
battery - switch - switch - light
0 1 1
battery - switch - switch - light
1 0 1
battery - switch - switch - light
1 1 10
battery - switch - switch - lightMuch simpler and a lot fewer switches
Now to the second issue, how would we add two double digit numbers using only 0 and 1?
We could it this way:
00 00 00
battery - switch - switch - light
00 01 01
battery - switch - switch - light
...
11 11 110
battery - switch - switch - lightBut that’s still a lot of switches, can we do it with fewer?
Let’s see what could help:
For now we’ve worked with switches that are controlled by a human, but what if a switch could be controlled by a wire instead?
battery - switch
| |
|-transistor-lightThis doesn’t seem very useful at first, but the implications are necessary to be able to build large systems.
Say we want to know both if someone is ready, and if everyone is ready, previously we would need to have everyone keep two switches:
Person A At least 1 is ready
batter +-[switch] --+ light
+-[switch] |
| | |
+--o--------+ |
| | Person B |
| --[switch]---- Both are ready
+----[switch]------lightBut now with this transistor, everyone only needs to worry about a switch again
Person A At least 1 is ready
batter +-[switch] -+-----|
| | transistor--+light
| | |
| | transistor-|
| | |
| Person B | |
+-[switch]--o-------+-----------|
| | |
| +-------| |
|----------------transistor--transistor-light Both are readyNow that we have only two digits 0 and 1, here’s another trick, what if when the switch is off, we consider it to represent 0 and when the switch is on, we consider it to represent 1?
First #
batter +-[switch] -+-----| #
| | transistor--+light
| | |
| | transistor-|
| | |
| Second # | |
+-[switch]--o-------+-----------|
| | |
| +-------| |
|----------------transistor--transistor-light Second #When you do long addition, you have the concept of carrying to the next column:
1
123
348
---
471What if we did a similar thing?
First #
batter +-[switch] -+-----| #
| | transistor--+light
| | |
| | transistor-|
| | |
| Second # | |
+-[switch]--o-------+-----------|
| | |
| +-------| |
|----------------transistor--transistor-light Carry
First #
batter +-[switch] -+-----| #
| | transistor--+light
| | |
| | transistor-|
| | |
| Second # | |
+-[switch]--o-------+-----------|
| | |
| +-------| |
|----------------transistor--transistor-light Carry