Silicon to Scripting 3
Invert
Looking at the NAND truth table
| A | B | Output |
|---|---|---|
| F | F | T |
| T | F | T |
| F | T | T |
| T | T | F |
we can try to reduce it into the INV truth table.
| A | Output |
|---|---|
| F | T |
| T | F |
If we look at the first and last row of the NAND table, it looks similar to the INV one, we just need to duplicate the input, which we can do.
And
Looking at the NAND and AND truth tables next to each other:
| A | B | NAND | AND |
|---|---|---|---|
| F | F | T | F |
| T | F | T | F |
| F | T | T | F |
| T | T | F | T |
we can see that when NAND is true, AND is false, and vice versa.
We can simply invert the output of NAND with an INV.
Or
Looking at the truth table for OR, we can see that instead of the 3-1 pattern on the output, it is a 1-3 pattern.
| A | B | Output |
|---|---|---|
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | T |
We can’t just invert the output.
instead we can invert the inputs of a NAND to turn it into a 3-1 pattern.
Conveniently, this is the solution.
Xor
Moving onto XOR, it looks very similar to OR, except when both inputs are true, it outputs false.
| A | B | Output |
|---|---|---|
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
We can start with an OR, and then try and find some component to AND with the output of.
We need something that outputs false when both inputs are on: NAND.
