81 lines
3.2 KiB
Markdown
81 lines
3.2 KiB
Markdown
---
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categories:
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- Electronics
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- Hardware
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tags: [logic-gates, binary, memory, clock]
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---
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# 3-bit Counter
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To demonstrate the use of
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[Flip-Flops](/Electronics_and_Hardware/Digital_circuits/Flip_flops.md) we will
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create the circuit for a 3-bit counter. This simply counts up from 0 to 7
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because 7 is the maximum decimal number we can create with three bits ($2^3$):
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| Binary | Decimal |
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| ------ | ------- |
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| 000 | 0 |
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| 001 | 1 |
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| 010 | 2 |
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| 011 | 3 |
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| 100 | 4 |
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| 101 | 5 |
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| 110 | 6 |
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| 111 | 7 |
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The circuit will have three memory components, each representing one bit of the
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3-bit number. When the
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[clock pulses](/Electronics_and_Hardware/Digital_circuits/Clock_signals.md), the
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3-bit number increments by one. We need to synchronise the operation with a
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clock because each bit by itself is meaningless, it only gains meaning by the
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relation it sustains to the other two bits hence it must be kept in sync with
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them.
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We can derive the circuit arrangement by analysing the outputs of a flipflop at
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each pulse:
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| Combined bits | Q2 | Q1 | Q0 | Decimal |
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| ------------- | --- | --- | --- | ------- |
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| 000 | 0 | 0 | 0 | 0 |
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| 001 | 0 | 0 | 1 | 1 |
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| 010 | 0 | 1 | 0 | 2 |
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| 011 | 0 | 1 | 1 | 3 |
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| 100 | 1 | 0 | 0 | 4 |
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| 101 | 1 | 0 | 1 | 5 |
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| 110 | 1 | 1 | 0 | 6 |
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| 111 | 1 | 1 | 1 | 7 |
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If we look at the pattern of each flip-flops' output we notice the following:
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- _Q0_ toggles on every pulse
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- _Q1_ toggles every time _Q0_ was previously 1
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- _Q2_ toggles when both _Q1_ and _Q0_ were previously 1
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This means that to construct a circuit that displays this behaviour we just have
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to use a
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[T flip-flop](/Electronics_and_Hardware/Digital_circuits/Flip_flops.md#t-flip-flops)
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since the only state change we need is a single bit toggle three times that
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retains its value.
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Using these pulse patterns we can construct a circuit as follows:
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<iframe src="https://circuitverse.org/simulator/embed/3-bit-counter-d33846e3-7538-427d-b4cc-dc64fdaf0af3?theme=default&display_title=false&clock_time=true&fullscreen=true&zoom_in_out=true" style="border-width:; border-style: solid; border-color:;" name="myiframe" id="projectPreview" scrolling="no" frameborder="1" marginheight="0px" marginwidth="0px" height="500" width="600" allowFullScreen></iframe>
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<br />
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> Remember from the table: Q2 is the most significant bit and Q0 is the least
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> significant bit so we should read the output in the interactive circuit
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> backwards, reversing the order. Then we will see that the cicuit is cyling
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> through 0-7
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This is how the circuit works:
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- All three flip-flops are connected to the same clock signal so that they are
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synchnonised
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- Because _T0_ is connected to the voltage source _Q0_ toggles every time the
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clock pulses
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- _T1_ is connected to _Q0_ so a clock pulse causes _Q1_ to toggle only when
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_Q0_ is high in line with the table
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- _T2_ is connected to _Q0 AND Q1_ so _Q2_ only toggles on a clock pulse when
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_Q0_ and _Q1_ are both high
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