flipfloplogic-gatespnptransistors
I only have 5 PNP transistors and I want to build two AND gates. (for a T Flip-Flop) What would be the simplest way to make an AND gate using PNP transistors? (It can't use more than 2 transistors)
This is the only way I found, but it uses way too many transistors.
You have to keep transistors and gates apart.
Four transistors is not bad to store a bit of data. If you would use a couple of gates you'd need at least 8. (A 2-input NAND gate consists of 4 transistors.) An SRAM cell is basically two inverters connected back to back, so that they one keeps the level of the other alive. One inverter consists of 2 transistors, so that's 4 in total.
Actually it's possible to use even less hardware to store a bit, and that's what DRAM does: it stores a bit as a voltage level in a capacitor. This means that you can get a lot more data in a square mm of DRAM than in an SRAM. Unfortunately the capacitor voltage leaks away, so the DRAM has to be refreshed continuously.
Assume ideal logic gates (no propagation delay) like this (image from wikipedia):
We know that the output of NOR gate is 1 if and only if both inputs are 0; and 0 otherwise.
When S = 1, Q = 1 and therefore \$\bar{Q} = 0\$; when R = 1, Q = 0 and \$\bar{Q} = 1\$.
But if you set both R and S to 1 we have that Q = 0 and \$\bar{Q} = 0\$ at the same time. This contradicts the relation \$Q = \bar{Q}\$. In the real world one of the gates will reach the 1 state first and the result will be unpredictable.
For the NAND-based RS flip-flop the same can be shown when R = S = 0, by writing the logic equations appropriately.
Best Answer
A good way to build gates with limited numbers of transistors is to use RTL (resistor-transistor logic) techniques. For example, here is a NAND gate, which can be converted into an AND gate with an inverter:
simulate this circuit – Schematic created using CircuitLab
The fan-in and fan-out capabilities of this type of logic are not great, which is why it was abandoned once the development of ICs made the incremental cost of transistors essentially negligible. But it can be used to build moderately complex logic circuits if you don't care too much about the speed.