# Boolean circuit diagram help

#### Hawkeye87

Joined Oct 7, 2008
52
I think i got the right answer on the Boolean equation diagram, but i need someone to check my work. The question states to draw a circuit diagram for the following equation.

A'C'D + BC'D + A'BD + AB'CD

My diagram has three 3 input AND gate, a 4 input AND gate, 5 inverters and 3 OR gates. Correct?

#### mik3

Joined Feb 4, 2008
4,843
You dont need 3 OR gates, you need one with four inputs. However, if you dont have one you can use 3 2-input OR gates to make a 4-input gate.

#### Hawkeye87

Joined Oct 7, 2008
52
Would anyone happen to have the book by Texas Instruments called TTL Logic Data Book to reference the chips that i got? I chose the 74LS04 as the inverter. The 74LS11 as the triple 3-input AND gate. A 74LS21 as a dual 4-input AND gate. And a 74LS32 as the quadruple 2-input OR gate. The only question i have is what would the output be?

#### MareBear

Joined Oct 29, 2008
22
are you using De Morgan's theorem already? if so it would be different, if not then that is correct (if it doesn't state how many inputs the gates have then you can use 4input OR's and AND's)

you don't need all the OR gates, you can use only 1, and the 2 AND gates can be replaced by 1 AND gate which I drew, depending on your professor is what you would have to draw.

#### scubasteve_911

Joined Dec 27, 2007
1,203
Marebear,

You're very nice for doing that for the OP

Steve

#### Hawkeye87

Joined Oct 7, 2008
52
We're actually using k-maps and deriving the truth table from the map, as well as the standard logic diagram.

#### scubasteve_911

Joined Dec 27, 2007
1,203
Hawkeye,

Actually, you need the truth table in order to create the K-map. The K-map is a logic reduction tool.

Steve

#### veritas

Joined Feb 7, 2008
167
The benefit of using a K-map is that you can quickly derive an equation with only two levels of logic, resulting in a fast circuit. MareBear's diagram, while it may have fewer gates, has four levels of logic propagation.

It's a tradeoff between space/cost and speed/ease

#### Hawkeye87

Joined Oct 7, 2008
52
where you highlighted the OR with the two arrows, what are you meaning by that. also, what happens to the output of the 4 input and gate on the bottom?

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#### Hawkeye87

Joined Oct 7, 2008
52
we're actually implementing these circuits in labs and we have to derive everything from a word problem.

#### scubasteve_911

Joined Dec 27, 2007
1,203
You can use either the 4-input gate, or the other three gates she is pointing to.

Steve

#### MareBear

Joined Oct 29, 2008
22
where you highlighted the OR with the two arrows, what are you meaning by that. also, what happens to the output of the 4 input and gate on the bottom?
you can do either or, use 2 AND gates or just use 1 depending on the #of inputs your AND gates have.