Building logic gates

Sep 16, 2023 (One bit computer)

This is a gate level diagram of the one bit CPU:

Not much is new here, it has an ALU, a few registers, a fairly standard decoder and some OR gates to drive the ALU. Together they implement all 16 of the instructions from the first post:

Opcode	Name	Function
0000 0	NOP	Does nothing
0001 1	LD	Load the bus into the accumulator
0010 2	LDC	Load the complement of the bus into the accumulator
0011 3	STO	Writes the accumulator on the the bus
0100 4	STOC	Writes the complement of the accumulator on the bus
0101 5	OEN	Loads the OEN register from the bus
0110 6	ADD	Adds the accumulator to the bus, using the carry register to store the carry
0111 7	XNOR	XNORs the accumulator with the bus
1000 8	XOR	XORs the accumulator with the bus
1001 9	AND	ANDs the accumulator with the bus
1010 A	OR	ORs the accumulator with the bus
1011 B	ONE	Forces a one into the accumulator and a zero into the carry
1100 C	TWO	Forces a zero into the accumulator and a one into the carry
1101 D	JMP	Strobes the jump flag
1110 E	SKZ	Skips the next instruction of the accumulator is zero
1111 F	RET	Skips the next instruction and strobes the return flag

The diagram is drawn with logic gates, describing abstract logic, like “The output should be true if and only if all of the inputs are true”. (AND gate). While logic gates can be built out of almost anything, including flowing liquids, interlocking metal plates, or even dominoes, transistors are by far the most practical option. They are cheap, easy to use, reliable and extremely fast.

Before creating any gates, we need to decide on how to represent a true/one and a false/zero in an electrical circuit: I have, completely arbitrarily, chosen that true will be 5 volts, and false will be 0 volts. As for the transistor, I used the 2N3904 but most other NPN transistors will work just fine¹.

A NPN transistor will only allow current flow between the collector and emitter (AKA turn on) if current is flowing between the base and the emitter.² With a grounded emitter as shown, the transistor will ground the collector when current is going into the base.

Two resistors, on on the base and another on collector can turn the transistor into a useful gate:

If the input is at 0 volts, no current will flow into the base, and the resistor at the will pull the output to 5 volts. If the input is at 5 volts, current will flow into the base, allowing current to flow from the collector to ground, pulling the output to 0 volts. This is a NOT gate: The output will only be true (5 volts), if the input is false (0 volts).

A more complex gate can be built by adding another transistor³:

Both transistors can pull the output to zero if their corresponding input is at 5 volts. The result is that the output is only 5 volts if neither of the inputs are. In other words, this is a NOT OR, or NOR gate.

A NAND gate can be built similarly:

Here, both transistors have to able to conduct to pull down the output, so the output is 5 volts unless both of the inputs are, so this is a NAND gate.

NAND and NOR have the interesting property, they can be combined to create arbitrarily complex logic, so are all that is needed to build any computer, but to keep the part count low, I will be using some more complex gates, like an (a AND b) NAND (c OR d) gate:

Despite the complexity, this gate works the same way as all the others: The output is 0 volts if there is a path of turned on transistors from the output to ground.