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Binary Counter

History Of The Computerflip-Flops - A Fundamental Counter

Flip-Flops - A basic counter

We seemed on the Binary system, and fundamental pc logic components, in previous articles, "It's a binary world - how computers depend" and "How computer systems add - a logical strategy".

Now we will mix {two} components of these articles to look at a counter. Another frequent logic aspect in a pc is a counter or timer. This could b to depend items going past a sensor on an meeting line, or possibly a count-down timer. For example, in case you have a late mannequin washing machine it will have a simple laptop using a depend down timer to present 10 minute wash cycle, etc.

There are a number of varieties of counter, almost all of which use a basic component of electronics, the Flip-Flop. And also you thought they had been rubber footwear English people put on to the bathe or the beach. (At this point Australians say "I thought they were called thongs").

OK again on topic. The flip-flop is as previous as electronics, and is a basic example of the binary system. It has {two} attainable steady states, A or B, and may be 'toggled' from one state to the other, identical to a 'push-on, push-off' switch. It was initially made with {two} vacuum tubes (or one, for example a double triode).

It normally has {two} outputs, one being the complement of the other. That's,if one output(A) is a logic 0, the opposite(B) is a logic 1, and vice-versa. The input, or Toggle(T) is at logic zero till a pulse from a sensor, for instance, comes along. This pulse takes the logic state to 1, then again to 0. The toggle effect, causing the Flip-Flop to flip, is definitely the CHANGE from 0 to 1.

In logic terms the flip-flop is made up utilizing AND and OR gates, in logic cicuitry it's just a 'black box' labelled FF. Several FFs may be grouped into yet another black box, a counter, timer, or multivibrator.

We are able to make up a Reality Desk, which we have used before. In the event you recall, a fact desk tells you what the Output will probably be for all attainable Inputs.

TRUTH TABLE for Flip Flop - Toggle (C)hange,- Outputs A and B.

INITIAL STATE
T B A
zero 1 zero 'A' output is zero

PULSE 1
T B A
C 0 1 'A' output is 1

PULSE 2
T B A
C 1 0 'A' output is zero

Now we string some flip-flops collectively to make a counter. Say we have now a sensor on a beer bottling machine, which has to rely 5 bottles before switching the feed, we have to count up to 5, or one zero one in Binary. We will need 3 flip-flops, for binary bits 0,1 and a couple of, akin to decimal bit value of 1,2 and 4.

We will take the A output of the three flip-flops to a decoder black field, which we will use to detect when we get to 5, then switch the feed. The B output of flip-flop zero is passed to the toggle enter of flip-flop 1 by way of an AND gate, so the next pulse from the sensor (which matches to all three flip-flops) at this AND gate will toggle the flip-flop, depending on the worth of the B output, zero or 1. Similarly the B output of flip-flop 1 goes to the toggle of flip-flop 3 through an AND gate.

Our 3 Flip-Flops now give you a fact desk like this:-

INITIAL STATE
FF2 FF1 FF0
TBA TBA TBA
010 010 010 'A' outputs 000 - 0

PULSE 1
FF2 FF1 FF0
TBA TBA TBA
C10 C10 C01 'A' outputs 001 - 1

[The (C)hange flips FF0 (at all times). FF1 & FF2 are blocked by the AND gate which wants a zero input from the earlier FF 'B' output AND the pulse change.]

PULSE 2
FF2 FF1 FF0
TBA TBA TBA
C10 C01 C10 'A' outputs 010 - 2

[The (C)hange flips FF0 (always). FF1 flips beacause the 'B' output from FF0 is a 0 when the Pulse arrives. FF2 is blocked as before.]

PULSE three
FF2 FF1 FF0
TBA TBA TBA
C10 C01 C01 'A' outputs 011 - three

[FF0 flips, FF1 is blocked once more,as is FF2.]

PULSE four
FF2 FF1 FF0
TBA TBA TBA
C01 C10 C10 'A' outputs 100 - four

(FF0 flips, FF1 flips, FF2 flips.)

PULSE 5
FF2 FF1 FF0
TBA TBA TBA
C01 C10 C01 'A' outputs one zero one - 5 depend complete!

[FF0 flips, FF1 and FF2 are blocked.]

This counter can rely as much as 111, 7 decimal, it then resets to 0. A few interesting points to note are:-

1. FF0 flips each pulse. FF1 flips each 2 pulses. FF2 flips each four pulses etc. These facts can be used to make up a divider, which might be cascaded. For example the 4 pulse output can go to a second counter which also offers a four pulse output, totalling 16. This may be expanded to make up a decadic counter by decoding a count of 1010 (10 decimal) and utilizing this to toggle the next counter, etc. What about 60 and 12 for your digital watch?

2. Take a look at the 'B' outputs from the counter. In sequence the values are:- 111, a hundred and ten, one hundred and one, a hundred, 011, 010 (7,6,5,4,3,2 decimal). See the sample? That's proper - a countdown timer! We'll be utilizing this in a later article.

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