Saturday, February 4, 2017

Hints for Nand2Tetris Chapter 1 Exercises

I have already done Chapters 1 to 8 of Nand2Tetris last 2013. But I want to finish it. I have decided to do everything all over again.

I am not allowed to put online my solutions to the Nand2Tetris exercises. So what I'm going to do instead is to give some hints on how to solve them.

Here are the hints for the Chapter 1 Exercises:

1. Not gate - look at the Nand truth table; notice the output when both a and b are the same

2. And gate - use your newly created Not gate (and the Nand gate of course)

3. Or gate - we can use the idea from the Canonical Representation presented on page 9. But instead of focusing on the 1 outputs of the Or function, let's focus instead on the 0 output.

The Or function has only one 0 output.

This means that we can be able to create an Or gate without using an Or gate. haha
We can solve this using the And and Not gates

"We will Not the And."

4. Xor gate - we can now use the Canonical Representation from page 9.

5. Multiplexor (Mux) - same as #4; use the Canonical Representation from page 9

6. Demultiplexor (DMux) - use truth table to determine when a and b will be 1; then use the Canonical Representation

7 to 10. Multi-Bit gates (Not16, And16, Or16, Mux16) - read "A.5.3 Busses" of the Appendix to know more about how to solve these.

Do something like this, for example, for the Multibit Not gate:

    Not(in=in[0], out=out[0]);
    Not(in=in[1], out=out[1]);

    Not(in=in[9], out=out[9]);

11. Multi-Way Or (Or8Way) - use Or gates and internal pins (see A.5.2 of Appendix A for an explanation for internal pins)

12 Multi-Way/Multi-Bit Multiplexor

       12.a (Mux4Way16) - use Mux16 and temporary internal pins

       12.b Mux8Way16 - similar to 12.a but also use Mux4Way16

13. Multi-Way/Multi-Bit Demultiplexor - quite similar to 12.a and 12.b

       13.a DMux4Way - Use DMux and internal pins

       13.b DMux8Way - same to 13.b but also use DMux4Way 

If you have any comments or corrections or ideas on how to make the hints better, please tell me. Thanks!

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