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Posted on 2002-06-20

how can combinatorics be used in logic circuit design

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Logic circuits are binary circuits. A single binary circuit can only be either 0 or 1. If you combine two binary circuits, you have 4 possibilities: 00,01,11,10.

3 binary circuis have 8 states and so on. You use combinatorics to know how many states a logic circuit has and to list them.

When you build a logical gate with transistors, each transistor can eiter be 0 or 1. So you use combinatorics to know all the possible states: "what is the output if the input is ..."

A binary system of n bits has 2^n states. If your bit could assume 3 states, 0, 1 and 2, then your n-bit system would have 3^n possibilities. I used combinatorics to calculate that.

Combinatorics, mainly, asks ans answers questions of the type "how many different ways exist to do something under various assumptions or constraints and counts these ways". The only sensible question of that type that might exist within Logic cirquit design is "how many different ways exist to realise a specific logic function". You use De Morgan and you create! But then, you do not want just to count them, but to design the solutions and select the optimal based on some criteria, usually the least number of gates. Some input from you dear ogom will help drive this discussion towards a sensible end.

Regards

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