Truth Table -> 3 output -> boolean expression -> circuit (DIGITAL LOGIC AND COMPUTER HARDWARE)

Thread Starter

judyfinny

Joined Feb 26, 2016
8
So I created a boolean expression based on the truth table. There are 3 output and three 4 input in the truth table. I have always seen one output and I know how to create a circuit with the boolean expression. But for the lab, I got three expression and we have to use that to create only NAND gate circuit. I am not sure how to use three different expression and make a NAND gate circuit. so these are the expression QQ: (y = AC + BCD + ABD) ; PP: ( y = A'B'C + A'CD' + AB'C' + AC'D' + A'BC'D + ABCD); CC (y = B'D + BD').
The question is to design realizations of the circuit using 1. only NAND gates 2. only NOR gates 3. AND, OR, and NOT gates.
I don't need an answer for this. But if you could explain how to use three different boolean expression to create one big NAND only circuit, that would be great. Thank you.
 

RBR1317

Joined Nov 13, 2010
509
You should apply DeMorgan's Theorem to convince yourself that a NAND gate is also an OR gate with negated inputs. That makes the NAND gate especially useful for building Sum-of-Products logical expressions (AB+CD). Likewise, a NOR gate is also an AND gate with negated inputs, and is useful for building Product-of-Sums logical expressions (A+B)(C+D). Note that negation of an output can be cancelled by a negated input.

My usual design technique is to draw the logical expression as a circuit diagram using AND/OR/NOT gates, then add pairs of inversion circles to the ends of a signal line, or move an inversion circle from an output to an input (or the reverse) until the gate types are all-NAND or whatever is necessary. After a while doing this you will just 'see' an OR gate with negated inputs as a NAND gate without having to redraw it.
 

WBahn

Joined Mar 31, 2012
24,970
So I created a boolean expression based on the truth table. There are 3 output and three 4 input in the truth table. I have always seen one output and I know how to create a circuit with the boolean expression. But for the lab, I got three expression and we have to use that to create only NAND gate circuit. I am not sure how to use three different expression and make a NAND gate circuit. so these are the expression QQ: (y = AC + BCD + ABD) ; PP: ( y = A'B'C + A'CD' + AB'C' + AC'D' + A'BC'D + ABCD); CC (y = B'D + BD').
The question is to design realizations of the circuit using 1. only NAND gates 2. only NOR gates 3. AND, OR, and NOT gates.
I don't need an answer for this. But if you could explain how to use three different boolean expression to create one big NAND only circuit, that would be great. Thank you.
Take the circuits for each output and implement them using only NAND gates.

Done.

Now, there may well be some overlap between the logic equations that would allow you to share parts of it and reduce the gate count, but nothing indicates that this is expected or required, so simply treat them as three different circuits from start to finish.
 

WBahn

Joined Mar 31, 2012
24,970
Am I understanding correctly that you have not simplified the Boolean equations, yet?
I don't think you can infer anything about that one way or the other.

From his original post:

So I created a boolean expression based on the truth table. There are 3 output and three 4 input in the truth table.
Cleaning this up just a bit, it should be: I have four inputs and three outputs, so I created boolean expressions based on the truth tables. There are three outputs, and thus there are three 4-input truth tables.
 

shteii01

Joined Feb 19, 2010
4,647
I don't think you can infer anything about that one way or the other.

From his original post:



Cleaning this up just a bit, it should be: I have four inputs and three outputs, so I created boolean expressions based on the truth tables. There are three outputs, and thus there are three 4-input truth tables.
That is true.
Back when I was getting my education, I might have had table like this:
ABCD|Q1|Q2|Q3
It is one table... but in reality it is three tables like you are saying.
 

Thread Starter

judyfinny

Joined Feb 26, 2016
8
You said 3 outputs.
I did not understand the part about the number of inputs. How many inputs are there?
Sorry, I just noticed the error. What I meant to say was there are 4 inputs and 3 outputs. (A,B,C and D are input and QQ PP CC are output). Sorry about that
 

shteii01

Joined Feb 19, 2010
4,647
Next step is to simplify the Boolean equations. Have you been taught any techniques to simplify them?

Like RBR said, you can just do three circuits and run all three circuits to the same ABCD inputs. Might take a bit of space.
 

WBahn

Joined Mar 31, 2012
24,970
Here is the truth table. This will make sense if I post the truth table i guess
There is absolutely no need for a 3MB file to convey three 4-input truth tables. This is just sheer laziness on your part. You can EASILY get that down to about 1% of that size with just a couple minutes effort. Instead, you expect members, many of whom have slow internet connections, to download a file that is literally a hundred times bigger than needed.

threeoutputs.jpg
 

shteii01

Joined Feb 19, 2010
4,647
There is absolutely no need for a 3MB file to convey three 4-input truth tables. This is just sheer laziness on your part. You can EASILY get that down to about 1% of that size with just a couple minutes effort. Instead, you expect members, many of whom have slow internet connections, to download a file that is literally a hundred times bigger than needed.

View attachment 101464
I blame cell phones. The effing things don't have any software to change image file size.
 

WBahn

Joined Mar 31, 2012
24,970
I blame cell phones. The effing things don't have any software to change image file size.
Then perhaps they should find a suitable platform with basic capabilities instead of imposing 100x the workload on everyone else just because it is more convenient for them.
 

Thread Starter

judyfinny

Joined Feb 26, 2016
8
Next step is to simplify the Boolean equations. Have you been taught any techniques to simplify them?

Like RBR said, you can just do three circuits and run all three circuits to the same ABCD inputs. Might take a bit of space.
Thank you :) I will do that.
 

Thread Starter

judyfinny

Joined Feb 26, 2016
8
There is absolutely no need for a 3MB file to convey three 4-input truth tables. This is just sheer laziness on your part. You can EASILY get that down to about 1% of that size with just a couple minutes effort. Instead, you expect members, many of whom have slow internet connections, to download a file that is literally a hundred times bigger than needed.

View attachment 101464
I am sorry. I didn't give much thought to that.
 
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