How can I simplify this circuit using boolean algebra for XOR and XNOR gates?

In summary, the conversation revolves around simplifying the boolean algebra expression M'(A'B'C+ABC')+M(AB'C'+A'BC) using different techniques such as K-maps, XOR and XNOR gates, and multiplexers. One person suggests using a PLA or a multiplexer for a simpler solution, while another tries to isolate a pattern using K-maps. However, it is noted that the suggested solutions may not be the simplest in terms of packaging on a breadboard or number of transistors in a chip. Overall, the conversation highlights different approaches to simplify the expression.
  • #1
speck
3
0
I want to simplfy M'(A'B'C+ABC')+M(AB'C'+A'BC) to as simple a circuit as possible.

I don't know the boolean algebra to simplfy the ABC terms. Help please, Speck
 
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  • #2
Tried K-maps?

From quick Venn inspection of (A'B'C+ABC') and (AB'C'+A'BC), I don't think you can simplify them further using AND, OR, NOT only
 
  • #3
K-map is how I initial got the Eq. , right, it won't simplify with AND, OR, NOT. I want to use XOR with XNOR gates. I would really like it to simplify to something like (AB Oplus C) using XOR, but it does not. Thks, Speck
 
  • #4
Does anyone think that the (A'B'C+ABC') part of the Eq. will reduce to (A Oplus B Oplus C)?
 
  • #5
By simple, do you mean the least number of packages? It's trivial with a single PLA, but you'd need a burner...
 
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  • #6
I tried to put it into XOR/XNOR but I really couldn't find any way.

P.S. (I learned this stuff few weeks ago, so all I know is that there should be checkboard pattern)

Now that I said that I realized that there is infact a pattern and it is easier to isolate it when you look at it. You got to approach it differently.
See K-Map When A = 0 and C = 1
A = 1 C = 0

I get something like

A!C!(B XOR M) + A!C (M XOR B)

So far, I look at K-Map and try to isolate 2 literal K-Maps that look like XOR and "and" it with conditions like A = 1 and C = 0 .. It works so far
 
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  • #7
Another PLA-type cheater's answer: use a multiplexer. Input ABCM as the addresses, hardwire the 16 inputs to 1 or 0 to synthetise the desired logic function. The 4067 is such a 16-to-1 mux-demux and seems to be still relatively common (hey, I just feel younger!). One single package, no programming needed.

For a non-cheater answer, you'll have to wait a bit more. M and B have similar roles, as do A and C, so combining these pairs first could bring something.
 
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  • #8
(A xnor C) nor (B xor M)
please check!

It's not "the simplest" form for the number of packages on a breadboard.

In a chip, I guess it's not the minimum number of Mos neither, as an xor or an xnor needs two inverters and 8 transistors, and a 16-to-1 mux also needs one inverter per input and this function consumes 16 N-channels and 16 P-channels.

Well, this form must be the simplest in the mind of some teacher at least.
 
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1. What is a logic gate XOR?

A logic gate XOR (Exclusive OR) is a digital logic gate that outputs a "true" value only when exactly one of its inputs is "true". It outputs a "false" value when both inputs are "true" or both inputs are "false".

2. What is the symbol for a logic gate XOR?

The symbol for a logic gate XOR is a plus sign inside a circle, with two inputs and one output. It can also be represented as a triangle with a curved base, with one input on each side and the output at the top.

3. What is the truth table for a logic gate XOR?

The truth table for a logic gate XOR is as follows:

Input A Input B Output
0 0 0
0 1 1
1 0 1
1 1 0

4. What is a logic gate XNOR?

A logic gate XNOR (Exclusive NOR) is a digital logic gate that outputs a "true" value only when both of its inputs are either "true" or "false". It outputs a "false" value when one input is "true" and the other is "false".

5. What is the difference between a logic gate XOR and a logic gate XNOR?

The main difference between a logic gate XOR and a logic gate XNOR is that the XOR gate outputs a "true" value when exactly one of its inputs is "true", while the XNOR gate outputs a "true" value when both inputs are either "true" or "false". Additionally, the symbols for these gates are different, with the XOR gate having a plus sign inside a circle and the XNOR gate having a plus sign inside a triangle with a curved base.

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