8 way OR gate in Hack's HDL language

Question

i'm a first year computer science student and i've found myself stuck on one particular part of the assignment. We are tasked to create several gates in hack's HDL in various ways. I had little to no trouble with most of them but i found myself stuck on the 8 way OR.

No matter how many times i've tried to come up with a solution, the test script always fails for the input values 00000001. I know why it does that and why it doesn't work, but i have zero clue about what i could do to get around it

Here's some iterations of the code i've tried using:

//Latest one
CHIP Or8Way {
    IN in[8];
    OUT out;

    PARTS:
    Nand(a = in[0], b = in[1], out = or1);
    Nand(a = in[2], b = in[3], out = or2);
    Nand(a = in[4], b = in[5], out = or3);
    Nand(a = in[6], b = in[7], out = or4);

    Nand(a = or1, b = or2, out = inA);
    //Nand(a = inA, b = inA, out = notINA);
    Nand(a = or3, b = or4, out = inB);

    Nand(a = inA, b = inB, out = out);
    //Nand(a = outpre, b = outpre, out = out);//i commented out these because i was trying to negate one of the inputs in the final Nand so that there wouldn't be a case where both 1s become zeros
}

//This is the iteration i've been stuck on trying to get working for the longest
CHIP Or8Way {
    IN in[8];
    OUT out;

    PARTS:
    Nand(a = in[0], b = in[0], out = not0);
    Nand(a = in[1], b = in[1], out = not1);
    Nand(a = in[2], b = in[2], out = not2);
    Nand(a = in[3], b = in[3], out = not3);
    Nand(a = in[4], b = in[4], out = not4);
    Nand(a = in[5], b = in[5], out = not5);
    Nand(a = in[6], b = in[6], out = not6);
    Nand(a = in[7], b = in[7], out = not7);


    Nand(a = not0, b = not1, out = mid1);
    Nand(a = not2, b = not3, out = mid2);
    Nand(a = not4, b = not5, out = mid3);
    Nand(a = not6, b = not7, out = mid4);

    Nand(a = mid1, b = mid2, out = orA);
    Nand(a = mid3, b = mid4, out = orB);


    Nand(a = orA, b = orB, out = out);
}

The amount of headaches this has given me is embarassing

Like i mentioned in the code comments i've first tried to negate one of the final inputs, then i tried to negate some more or to change up my grouping logic all with no luck

Answer 1

First principals: de morgan's law says A or B == (not A) NAND (not B) expanding that out for all 8 instead of just two might have a way to reduce gates, but the direct approach would be to realize A or B or C or D or ... H == (A or B) or (C or D) or (...) to get the first set you should do what you're doing above but then when you want to combine those mid values, you need to negate them and use a nand... i.e.

//This is the iteration i've been stuck on trying to get working for the longest
CHIP Or8Way {
    IN in[8];
    OUT out;

    PARTS:
    Nand(a = in[0], b = in[0], out = not0);
    Nand(a = in[1], b = in[1], out = not1);
    Nand(a = in[2], b = in[2], out = not2);
    Nand(a = in[3], b = in[3], out = not3);
    Nand(a = in[4], b = in[4], out = not4);
    Nand(a = in[5], b = in[5], out = not5);
    Nand(a = in[6], b = in[6], out = not6);
    Nand(a = in[7], b = in[7], out = not7);


    Nand(a = not0, b = not1, out = mid1);
    Nand(a = not2, b = not3, out = mid2);
    Nand(a = not4, b = not5, out = mid3);
    Nand(a = not6, b = not7, out = mid4);
     //change from your anser:
    Nand(a = mid1, b = mid1, out = not_mid1);
    ...
    Nand(a = not_mid1, b = not_mid2, out = mid1_or_mid2)
    Nand(a = not_mid3, b = not_mid4, out = mid3_or_mid4)
    Nand(a = mid1_or_mid2, b = mid1_or_mid2, out = not_mid1_or_mid2);
    Nand(a = mid3_or_mid4, b = mid3_or_mid4, out = not_mid3_or_mid4);

    Nand(a = not_mid1_or_mid2, b = not_mid3_or_mid4, out = out);
}