From a NAND Gate To Tetris

mikejuk writes "Long before the current crop of MOOCs (Massive Online Open Course) there was a course that taught you all you needed to know about computers by starting from the NAND gate and working its way up through the logic circuits needed for a computer, on to an assembler, a compiler, an operating system, and finally Tetris. Recently one of the creators of the course, Shimon Schocken, gave a TED talk explaining how it all happened and why it is still relevant today. Once you have seen what is on offer at http://www.nand2tetris.org/ you will probably decide that it is not only still relevant but the only way to really understand what computers are all about."

Comments

Re:Logic is Logic

[dkf]

AND, OR, NOT, NAND, NOR, XOR and XNOR are still the 7 basic logic elements that make up all digital electronics and programming.

Actually, real digital circuit design uses rather more elements than that, some of which can't be derived from those ideal elements either. Even excluding the clock generator (a thoroughly analog component in its core) there's still some really strange things you can usefully do with transistors that just won't model as anything simpler; my favorite is the arbitrator, it determines which signal rose (or lowered) first and which is used to connect together parts of a chip that use a common power supply but unsynchronized clocks. Simplistic digital theory says it can never work, but in reality it's very effective (and it depends on the fact that transistors are analog devices with some quantum mechanical behavior for disambiguating in the tricky cases. Mad, fun, mad fun!)

Re:Logic is Logic

[sFurbo]

You have 2 inputs that can each be 1 or 0, so there are 4 different inputs. For each of those, you have 2 possible outputs, so there are 2^4=16 different truth tables.

Of these, 8 are symmetrical in A and B (gives the same output for input (1,0) and (0,1)). Theses are AND, OR, NAND, NOR, XOR, XNOR, TRUE and FALSE

The remaining 8 are 4 sets of duplicates (if you switch A and B, we call the gate the same name). These are A, not-A, A AND NOT-B, and its negation, NOT-A OR B. The two last does not seem to be standard gates, so no, there are, in fact, two more non-trivial truth tables for two inputs.

Re:Logic is Logic

[famebait]

No, but it sums up all the useful/practical ones.
If you only have two inputs, there are only 4 rows in the table,:
| A | B |
| 0 | 0 |
| 0 | 1 |
| 1 | 0 |
| 1 | 1 |

This yields only 16 possible output columns:
0000 - does not vary with input
0001 - AND
0010 - not commutative
0011 - reacts only to A
0100 - not commutative
0101 - reacts only to B
0110 - XOR
0111 - OR
1000 - NOR
1001 - XNOR
1010 - reacts only to B
1011 - not commutative
1100 - reacts only to A
1101 - not commutative
1110 - NAND
1111 - does not react to input

That makes 6 potentialy desirable operations. The seventh is NOT, which takes only one input.
The not commutative ones could conceivably be put to useful work, but in physical designs the asymmetry is impractical, and you can trivially construct them from other gates if need be. In fact some of the useful ones ar also usually constructed from combinations of the others, and all of them *can* be constructed from combinations of NAND gates.