digital-logic
I'm just starting with digital-logic but I now face a little problem: I learned that AND, OR, NOT were basic gates and that one basic gate could not be made from a combination of two others. How comes that this combination:
produces an OR truth table from only AND and NOT gates?
You are confusing logical and electrical models.
A NOR gate is a NOR gate, with the truth tables as you show in your question. The entries in that table are logic values. Logic values are mathematical constructs, that have no intrinsic relation with the real world.
When you take let's say a 74HC00 chip it contains 4 2-pinput gates. With the by-convention standard assignment of voltage levels to logic values (0V=0 5V=1) those gates behave as NANDs. But when you use the less common assignment of 0V=1 5V=0 the same gates behave as NORs.
The table below is taken from the 74HC00 datasheet. It shows the truth table for a single gate, but note that it states that this table holds only when you use the standard assignment of voltage levels to logical values.
Summary: there is no such thing as a 'negative logic NOR gate'. There are NAND and NOR gates, which are mathematical constructs, and there are physical circuits. Whether a specifc circuit implements the NAND or the NOR function depends on your choice of which voltage level correspons to which logical value.
The best way to do this is to analyze each case separately. This gate has two input signals, so only four combinations to analyze. For each case write down the inputs and the resulting output. After the four cases, you have a truth table, which you say you already understand.
Here is the case with both inputs 0:
Both transistors are obviously off, so the pullup drives the output high.
Now do the (1,0) inputs case:
The bottom transistor is obviously off, so again the outut can only be high.
Case (0,1):
Case (1,1):
From these four cases you get the truth table:
In1 In2 Out
--- --- ---
0 0 1
1 0 1
0 1 1
1 1 0
which is the NAND function.
Best Answer
Whoever told you that was simply wrong. In fact, many logic families use just one kind of gate, especially in the early days. RTL logic families were basically all NOR gates, and DTL and TTL families are basically NAND gates. In either case, you can think of NOT as a single-input gate.
You can build any logic function at all from just NOR gates or just NAND gates. Entire computers have been built this way, including the earlier Cray supercomputers.
And don't forget that !(A + B) == !A & !B and that !(A & B) == !A + !B. Take the first equation and negate both sides, and you end up with your example: A + B == !(!A & !B).