For educational purposes, I put together a one-bit adder, the fundamental logic module which adds two bits together in a computer. There are three inputs, bit A, bit B, and the CIN or Carry In bit. There are two outputs, the SUM and the COUT or Carry Out bit.
Logic for One-Bit Adder
That image was taken out of this PDF:
One-Bit Adder Schematic
You can leave out the pull-down resistors if you would like. But be aware that when your inputs are floating, your outputs will also be unstable.
These are the ICs I used:
- CD4081BE (quad AND logic)
- CD4070BE (quad XOR logic)
- HD7432P (quad OR logic)
In retrospect it would have made more sense to use a CD4072 for the OR logic, just to stick with one family of logic chips. You could, but the pinout is not compatible with what is drawn in my schematic.
To make an eight-bit adder, you could just chain these together (minus the LEDs, of course), tying COUT from one module to the CIN for the next module. But you can see that there are unused gates on the chips, and it would reduce the chip count if you use those. On average, it takes 1.25 chips per bit. An eight bit adder requires four AND chips, four XOR chips, and 2 OR chips.
I am embarrassed to show the breadboard example, due to the messy jumper wires. But it works. In the photo I have one input bit and the CIN bit at logic high, which causes the COUT LED to light up but not the SUM LED.
One-Bit Adder Breadboard Example
That's pretty cool! I saw a guy who made a mechanical/liquid binary counter that was also pretty cool: