Number System
NUMBER SYSTEM
Why modern Electronic computers can only understand Binary numbers, why not Decimal numbers???
From the previous topic, Can machines understand Decimal numbers???
In order to implement Decimal numbers in a machine, we need components or devices that can have $10$ stable positions or states.
🌾Mechanical machines, use Gears with $10$ stable positions or states to implement Decimal numbers.
🌾Electro-Mechanical machines, use Ten position relay (Relay combined with gear using clutch) with $10$ stable positions or states to implement Decimal numbers.
🌾Hence it is possible to build a mechanical or electro-mechanical machines / computers that can support decimal numbers.
Electronic Computers:
To make electronic computers that can support decimal numbers in calculations, programming, storage, etc., we need electronic components or devices that can have $10$ stable states.
Electronic components:
Vacuum tubes:
- Vacuum tube was invented by John Ambrose Fleming in $1904$. In $1906$, Lee De Forest invented ‘Audion’ – a triode vacuum tube.
- It consists of three electrodes, a cathode, a control grid and an anode.
- When cathode is heated, it emits electrons and the anode which is positively charged, attracting the electrons towards it.
- The control grid located between cathode and anode can control the flow of electrons.
- When grid is negatively biased, it repels electrons, turns off the tube.
- From this we can say, vacuum tubes can only have two positions or states. Among them, ON position is stable and OFF position is astable.
BJT, FET:
- After vacuum tube, scientists invented Bipolar Junction Transistor (BJT), Field Effect transistor (FET) with similar working principle as vacuum tube.
- Both are having two states only (ON and OFF) – one stable and one astable.
🌾Flip-flop:Â
- Eventhough vacuum tubes have two states, one of them is astable. Hence an electronic device with two stable states was invented and named as Flip-flop.
- Flip-flop was invented by William Eccles and Frank Wilfred Jordan in $1918$, originally called as Eccles–Jordan trigger circuit.Â
- It was designed using two vacuum tubes.
Flip-flop has two stable states, $ON-OFF$
- A small trigger signal input is used to change the state, and that state will remain stable until it is disturbed.
- Nowadays, Flip-flops are designed using transistors and logic gates.
Only two stable states!!!
- After this much years, no electronic components that can have more than $2$ stable states were invented.Â
Electronics world stuck with $2$ stable states
- Since electronic components can only have $2$ stable states, we cannot build an Electronic computer (efficiently) that can understand decimal numbers.Â
- Hence scientists were in need to find a number system, that only have two base numbers.
A new number system!!!
- In $17^{th}$ century, Gottfried Leibniz proposed and developed a number system with only two base numbers. $$0\; and \; 1$$
- Since $bi=two$, the above number system is named as Binary number system or base-$2$ number system.
- Scientists adopted this binary number system to design and build machines with electronic components having $2$ stable states. $$OFF=0\; and \; ON=1$$.
🌾Hence we can safely say,