Background
A typical computer architecture is based on a set of elementary logic gates like And, Or, Mux, etc., as well as their bit-wise versions And16, Or16, Mux16, etc. (assuming a 16-bit machine). This project engages you in the construction of a typical set of basic logic gates. These gates form the elementary building blocks from which more complex chips will be later constructed.
Here is what i have learnt in this week.
1.Boolean laws
Any boolean function can be represented using an expression containing only NAND operations.
Proof:
-
NOT(x) = (x NAND x)
-
(x AND y) = NOT(x NAND y)
2.Hardware description language
In computer engineering, a hardware description language is a specialized computer language used to describe the structure and behavior of electronic circuits, and most commonly, digital logic circuits. Wikipedia
Here is the hdl code for the And gate (or chip).
/**
* And gate:
* out = 1 if (a == 1 and b == 1)
* 0 otherwise
*/
CHIP And {
IN a, b;
OUT out;
PARTS:
Nand(a=a,b=b,out=o);
Not(in=o,out=out);
}
Notice how And gate is built on Nand gate, … and Not gate, but actually Not gate is built on Nand gate as well. Nand is the atom gate, hence the course named Nand2Tetris.
Premitive Nand gate that be used to build other gates. Nand means not-And, the opposite of And gate.
| x | y | Nand | And | |
|---|---|---|---|---|
| 0 | 0 | 1 | 0 | |
| 0 | 1 | 1 | 0 | |
| 1 | 0 | 1 | 0 | |
| 1 | 1 | 0 | 1 |
3.Project: Logic gates
Enough for the theory, let’s get your hand dirty writing actual hdl codes. In this week, 15 gates are built can be categorized into 3 groups:
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Elementary logic gates (e.g: And, Or, Xor, …)
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16-bit variant of above gates (e.g: And16, Or16, …)
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Multi-way variants gates
Reference