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Suppose that I have designed an electrical digital circuit that contains only resistors, transistors, capacitors and diodes to implement some electrical device, but it contains many instances of these four electronic components that makes the electrical circuit complex, difficult to produce and this also makes the production of the electrical circuit and the electrical device too expensive.

Do already exist methods to minimize, reduce and simplify electrical circuits with only resistors, transistors, capacitors and diodes so I can implement the same electrical circuit, with same inputs, outputs and behavior with lesser and minimal number of these four electronic components?

If the methods exist then what are they then?

Can someone please give me reference to webpages that explain these methods in simple english and physics words?

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    \$\begingroup\$ This question is very broad. Can you say more about your case? For example, is this a digital or analog circuit? \$\endgroup\$
    – DanielSank
    Commented Aug 20, 2017 at 19:11
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    \$\begingroup\$ Good question. I will edit my question now and my circuit is digital. \$\endgroup\$
    – Erez Zrihen
    Commented Aug 20, 2017 at 19:12
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    \$\begingroup\$ This is an overbroad question, really about how all digital IC logic is designed. Maybe start reading here: electronics.stackexchange.com/questions/67598/… \$\endgroup\$
    – MarkU
    Commented Aug 20, 2017 at 20:15
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    \$\begingroup\$ This sounds like a "optimizing for area" problem. This is definitely done because it's standard in most EDA tools. If the circuit is pure digital, e.g. you only care about the logic, then there are tools that can do this for you, if you can represent the logic in a standard form like HDL. \$\endgroup\$ Commented Aug 21, 2017 at 3:57
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    \$\begingroup\$ But honestly, if your logic is complicated then your fewest-component solution could be a microcoded one, like a simplified CPU plus some program memory. This would allow the machine do calculate a complicated logic in a long time, and trade speed for component count. Then if you would need to build a CPU, why not just buy one? \$\endgroup\$ Commented Aug 21, 2017 at 4:08

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Suppose that I have designed an electrical digital circuit that contains only resistors, transistors, capacitors and diodes to implement some electrical device ...

Generally, digital devices don't use discrete components but there are a few standard exceptions. Most digital circuits use logic gates or microprocessors and these are almost exclusively integrated circuits.

So where do we use discrete components on digital designs?

  • Crystal controlled clocks use capacitors in conjunction with a crystal to generate a high frequency clock signal. There is nothing you can do to simplify this.
  • Many micro-controllers have an internal oscillator whose frequency is controlled by an external R-C combination. Again both of these are required.
  • Power-up reset circuits use an R-C circuit too. On power-up the capacitor holds the reset pin low for a few ms to give the power time to stabilise and to force the chip into correct initial state. The capacitor is charged by the resistor and at a certain threshold the reset is released and the chip can boot. Again, the R-C combination is the minimum requirement.
  • Diodes are unusual in logic circuits but, as many answers on this site will show, they can be used to perform simple logic such as ORing two signals and thereby avoiding the need for another chip.
  • Transistors tend to be used as current amplifiers or sometimes as level-shifters to interface between circuits on different voltages.

As with any design, it's hard to beat experience. There are times when the minimum component count approach (where some components perform several functions) may be worse than a modular design which is easier to understand, test, calibrate and debug.

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The normal way to implement digital circuits like, AND, OR, XOR, NOT and buffer is with integrated circuits like the 7400 or 4000 series.

Reference:

https://en.wikipedia.org/wiki/List_of_7400_series_integrated_circuits

https://en.wikipedia.org/wiki/4000_series

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I suggest you learn how the combinatorial-logic AND_OR_INVERT gates are implemented. Just one or two transistors used for certain "logic" functions.

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State diagrams and Karnaugh maps are used to reduce Boolean algebra expressions. Start by describing each output line as a Boolean expression using whatever inputs affect it. Some patterns might appear, leading to common terms across multiple equations.

Why are you restricted to non-IC components? Is this homework?

https://en.wikipedia.org/wiki/Karnaugh_map

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    \$\begingroup\$ This is not homework. I like low level more than the high level as I like the assembly programming language more than C# programming language for instance. \$\endgroup\$ Commented Aug 20, 2017 at 22:00

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