The term “combinational” comes to us from mathematics. In mathematics a
combination is an unordered set, which is a formal way to say that nobody cares
which order the items came in. Most games work this way, if you rolled dice one
at a time and get a 2 followed by a 3 it is the same as if you had rolled a 3
followed by a 2. With combinational logic, the circuit produces the same output
regardless of the order the inputs are changed.

There are circuits which depend on the when the inputs change, these
circuits are called sequential logic. Even though you will not find the term
“sequential logic” in the chapter titles, the next several chapters will discuss
sequential logic.

Practical circuits will have a mix of combinational and sequential logic,
with sequential logic making sure everything happens in order and combinational
logic performing functions like arithmetic, logic, or conversion.

You have already used combinational circuits. Each logic gate discussed
previously is a combinational logic function. Let’s follow how two NAND gate
works if we provide them inputs in different orders.

We begin with both inputs being 0.

We then set one input high.

We then set the other input high.

So NAND gates do not care about the order of the inputs, and you will find
the same true of all the other gates covered up to this point (AND, XOR, OR,
NOR, XNOR, and NOT).


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