# Converting my expression into cellular logic

#### u-will-neva-no

Joined Mar 22, 2011
230
Hello peeps, Below is my truth table for an even parity:

Decimal Parity A B C D
0 0 0 0 0 0
1 1 0 0 0 1
2 1 0 0 1 0
3 0 0 0 1 1
4 1 0 1 0 0
5 0 0 1 0 1
6 0 0 1 1 0
7 1 0 1 1 1
8 1 1 0 0 0
9 0 1 0 0 1
10 0 1 0 1 0
11 1 1 0 1 1
12 0 1 1 0 0
13 1 1 1 0 1
14 1 1 1 1 0
15 0 1 1 1 1

And here is my boolean equation:
F = A'B'C'D' + A'B'C'D' +A'BC'D +A'BCD' + AB'C'D + AB'CD' + ABC'D' +ABCD

I now have to convert this combinational system into cellular logic form. I have no idea how to do this...Thankyou for reading!

#### u-will-neva-no

Joined Mar 22, 2011
230
The title of the table corresponds to the bits, just that it is not alligned! Sorry about that!

#### Georacer

Joined Nov 25, 2009
5,182
What does "cellular logic" refer to? Do you mean that you want to use logic gates to build the parity generator circuit?

#### u-will-neva-no

Joined Mar 22, 2011
230
From my lectures, the cellular logic has been drawn my a "square box",or cell,
usually with two inputs, and you can cascade it into a series of identical functions. My issue is what should go inside the "box".

One example that I do understand was where I had to realise the cellular logic for a half adder circuit. Thus, I drew an XOR gate inside, where the two inputs could be chosen. For my above question, I do not recognise a type of gate configuration to but inside the cell

After writing all of the above, I just realised that iIcould have simply replied "yes"... lol!

#### Georacer

Joined Nov 25, 2009
5,182
Heh, yours is a common question and the answer is actually very easy.

Take a look a the XOR gate: Its TF is F=A'B+AB'. In other words, it gives a '1' when it gets {AB}={10} or {AB}={01}. Does that ring any bells? It's an odd parity detector!

And it's actually cascadable: A XOR B XOR C XOR D for example is a 4-bit odd parity detector.

The Mods lectured us lately about giving you guys ready solutions so I guess I 'll leave the rest to you. Come back with any questions.

#### u-will-neva-no

Joined Mar 22, 2011
230
Im still slightly confused! My first issue is that you stated that the XOR function is an odd parity detector. I read on-line that odd parity is when the total bits (including the parity bit) is odd, so is XOR an even parity detector? Please correct me if this is wrong!

Other than that, I now understand! Just as an aside, would the "real" cellular logic have some form of CMOS or TTL logic inside and can you buy standard XOR cellular logic cells?

#### u-will-neva-no

Joined Mar 22, 2011
230
^^ a slight contradiction in my post, ignore the "im still slightly confused" part!

#### Georacer

Joined Nov 25, 2009
5,182
If the XOR gate is an odd parity detector, isn't the NOT XOR an even parity detector? Think about it.

If you want to find the even parity of A,B,C and D, A XOR B XOR C XOR D will give you the odd parity. Complementing that expression with a NOT gate will invert the parity. If it's NOT odd, well, it's even!