# Questions tagged [boolean-algebra]

In mathematics and mathematical logic, boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Boolean algebra is used in the analysis and simplification of digital (logic) circuits

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### boolean confirm result

I have solve an exercise and I would like to know if I find the result right. Is there a way so I can check that my solution is right? I think this method is called De Morgan. I had this and I find ...
3answers
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### Trying to simplify a Boolean expression to $X + Y + Z$

Problem: Prove the following Boolean equation using algebraic manipulations: $$Y + \overline X Z + X \overline Y = X + Y + Z$$ Answer: $$LHS = Y + \overline X Z + X \overline Y$$ \begin{align*} LHS &...
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### How do you algorithmically calculate the booth recoding truth table for different radix?

Basically what I am trying to figure out is how one generates algorithmically the truth table for Booth's recoding for different radices of his algorithm. How would you generalize this into a truth ...
2answers
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### Simplyifying a Boolean Expression that has three variables in it

The following problem can be found at the following URL: Some problems related to digital logic It is problem number 26 on the webpage. Problem: Simplify the following expression using Boolean Algebra:...
2answers
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### Boolean algebra — minterms for 1:1 inputs and outputs

Let's say we have a truth table with two inputs (A, B) and one output (X). ...
1answer
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### Meaning of logic operation “ a' ”

I have found the following expression: c = (a'.b) what does it mean? I know a.b is a and b (...
3answers
108 views

### Why do we always implement the complementary of the boolean expression when we design a CMOS circuit?

I am new to implementing boolean expressions in CMOS form, and I understand that the "C" in CMOS stands for "Complementary", so it is an inverter circuit. What I don't understand ...
0answers
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### Combining MUX 4x1 to represent 5 variable function

I have the following function x’y’zw’v’ + x’yz’w’v’ + x’yzw’v’ + xy’z’w’v’ + xy’zw’v I should implement it using only 4x1 MUX (more than one allowed, of course). I'm clueless on how could I combine ...
0answers
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### How to implement a 2 digit BCD subtractor with only 2 7483s?

I need to build a 2 digit BCD subtractor with the limitation of only having 2 7483 (4 bit adders). Additionally, 20 > minuend >= subtraend. With those limitations in mind, i can see that if the ...
0answers
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### How to convert a Boolean expression from POS form to SOP form?

POS equation is given as F=pi(3,8,12). By converting POS to SOP form directly I get F=sigma(0,1,2,4,5,6,7,9,10,11,13,14,15) But according to the process given in the above picture F is given as F=...
1answer
58 views

### When do we use minterm over maxterm in real words example or vice versa?

This may sound stupid. We have minterms. It is a product of all variables in a function and that function has the property that it is equal to 1 on exactly one row of the truth table. What do we call ...
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### I need help finding out how to prevent my components from exploding (TinkerCad)

Basically, I'm making a logic circuit on TinkerCad and I need to turn on a seven-segment display but some of my components explode and I've got no idea how to solve this. The components I'm using are:...
1answer
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### Will the Boolean equation change when we reduce the CMOS transistors in a static CMOS logic?

We are doing a project about a multiplier. Two of my teammates are assigned to make the transistor level designs of the adders, subtractors and few barrel shifters. My prof has told me to make a ...
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### How to know whether addition has been done in a parallel binary adder?

I am little new to electronics and getting some high level overview of digital electronics. The question is that how to know whether addition has been performed in a logic circuit. For example I have ...
3answers
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### Karnaugh map: What values to combine?

I have obtained the Karnaugh diagram (pictured below) and now I'm trying to obtain the Boolean expression of K3 through this diagram. My inputs are Q1, Q2 and Q3. I'm trying to "group" 1's ...
1answer
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### Does the exclusive AND gate exist?

i have just received an assignment to identify what logic gate circuit of the given logic gate symbol indicates in the attached image. Parts a) and d) are easy, but are there gates like pictures b) ...
0answers
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### How do I verify my solution is correct for a circuit diagram?

The original problem: The trouble I'm having is that I'm not sure at all if my boolean expressions from the circuit diagram for (1) are correct; I also know that I ...
1answer
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1answer
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### Boolean Algebra: How do I implenent a 4 bit signed comparator

I'm studying for my digital electronics exam and I'm a bit lost here. The goal of the exercise was to build 2 4bit comparators out of single bit comparators, one using unsigned bits and the other with ...
1answer
52 views

### Using don't cares to reduce a function

We have the function: f = p'c' + pb' + qc With satisfiability don't cares given by SDC = {pb, q'b', qbc, q'*c'} The K-map for the function is : ...