Using a decoder and external gates design the combinational

Using a decoder and external gates. design the combinational circui defined by the following three boolean functions:

F1 = x\'yz\' + xz
F2 = xy\'z\' + x\'y
F3 = x\'y\'z\' + xy

/** So I did that, and I got F1 = minterms(2,5,7), F2 = minterms(2,3,4) and F3 = minterms(0,6,7).

My question is with building the circuit as I have a different solution than the books.

Here is my solution, the truth table returns the correct answer. HOWEVER, it is missing the enable.

Here is the books solution:

I don\'t want help solving this, I just want help understanding what the enable does exactly and why its a complement in this problem. I would also like to know why they are using a nand gate, especially at the end where I used an or gate. Is this all because of the enable? What is wrong about my answer as it yields the correct truth table?

EDIT***

So i see Nand Nand makes an OR and I understand that after doing the math by had.

SO that leaves just two questions.

1. Do i need an enable? and if I do, it can just connect to each one without being a complement correct?

2. What is the reasoning for using the nands as opposed to what I did. The way I did it seems a lot simpler, so im assuming there is logic behind doing it the other way.

thank you!

DO Dl 0 0 D2 D3 OF2 0 D4 0 DS F3 D6 D7 Combinational Analysis Table Expression Minimized x yz F1 F2 F3 0 0 0 0 0 1 0 1 01 0 0 1 10 0 1 0 0 0 10 1 0 1 0 0 1 10 0 01 1 1 11 0 1 Build Circuit

Solution

In modular arithmetic the set of congruence classes relatively prime to the modulus number, say n, form a group under multiplication called the multiplicative group of integers modulo n. It is also called the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. (Units refers to elements with a multiplicative inverse.)