# 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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### Is it necessary to have all variables of a boolean expression in its POS or SOP form?

For example, if we have a boolean expression, anything like: X= A′ B + CD + (A+B)′ [ACD + (BE)′ ] We know this can be CD + A'. ...
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### Why does NOR need one more output to the multiplexor but NAND not in ALU?

Recently, I was learning "Computer Organization and Design: The Hardware/ Software Interface" riscv 2nd Edition by "David A. Patterson" In appendix A, A-37 shows the question in &...
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### How should I proceed with implementing a multiple sequence detector FSM?

I was given the following question: Design a finite state machine (FSM), with not more than 4 states, that will detect more than one number of 1’s in the previous 3 samples. For example - ...
1 vote
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### How can I improve my ladder logic diagram of a vending machine?

I am trying to create a coffee and tea machine using a ladder logic diagram. There are small, medium, and large sizes. This is where I am now: Can you give me any ideas or corrections on how to ...
734 views

### Electrical counterpart: Logical not

I'm building a circuit where I must receive a signal from a logical not. More specifically, I'm looking for a real-life electrical circuit element/component that provides power/signal on the output ...
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### How can I convert boolean algebra to logic gates?

I have a very large boolean algebra equation that I designed in Logic Friday, but it got too complicated for it to turn into gates. Note that I am a programmer, not an electrical engineer, so please ...
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### How to express this logic circuit with output feedback as boolean expression?

Q1. How to express this circuit as boolean expression? It uses the output as input (feedback??) to part of the circuit. Is it a special type of circuit? Q2. How do I simplify it as Nand-only ...
1 vote
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### How do we get a -1 in a 1-bit ALU?

In the 1-bit ALU and the table that is shown below, as you can see, the output is -1 when F0 = 1, F1 = 1, ENA = 0, ENB = 0, INVA = 1, INC = 0. The table is taken from a book (Structured Computer ...
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### Logism: Further reducing number of logic gates in a circuit

I have this circuit attached below that has an arbitrary behavior. I want to reduce the number of gates more if possible. I've taken its expression and passed it through multiple boolean expression ...
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### How do I simplify the two boolean expressions?

I have the two expressions that I have already simplified as much as possible: C̅D̅ ∨ A̅B̅D ∨ A̅BC̅ AB ∨ AC ∨ B̅C̅ However, I know that you can simplify both expressions even further per KV diagram: ...
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### My logisim simulation of a sequential circuit using T Flip-Flop is stuck at 1-1-1

I have an assignment that required us to draw a logic diagram of this sequence using T-flipflops: The state diagram: I obtained this Boolean algebra expression using a KMAP: ... 1 vote
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### Can the output of a logic gate be split to serve as input for other logic gates?

In the textbook picture, they use 5 NOT gates, repeatedly splitting the R input only to have it go into a different NOT gate. Are you allowed to put the input of R into a single NOT gate, and split ...
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### Understanding OLD PEEL173 code

I have some code for a PEEL173 form the early 90's. I would like to understand the logic of this code, but I don't recognize this syntax. Question 1: Do you recognize the syntax of this language? What ...
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### Similarity in "carry and sum" and "difference and borrow"

i know carry and sum from all the sources i studied in YT (particularly KNOWLEDGE GATE) except neso academy that teaches using difference and borrow in same place as carry and sum Sources:- Knowledge ...
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### simplify Boolean function F(A, B, C, D) = ∑ m(0, 1, 3, 4, 5, 7,8,9 11, 13,14,15)

Hello just got stuck simplifying this boolean function using four variable K-Map. I have to simplify this boolean function in terms of sum of minterms. ...
123 views

### Logic gate: electricity, voltage and meaning [duplicate]

I am confused by this kind of diagram (simplest, NOT gate): ------1------___Gate Here___-------0-------- Because my book tends to talk about electricity. So if I ...
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### Transition table from state truth table

Assuming a simple binary state variable allocation can be made and that any unused states can be treated as don’t cares. How would I Design a corresponding transition table for this system including ...
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### Need help determining CMOS circuits with logic function Y [closed]

I am trying to determine which of the CMOS circuits in the question below have the logic function Y, but I am having trouble understanding how to do so. I have tried looking at the circuits and ...
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### Is my simplified Boolean expression correct?

I'm trying to simplify the following Boolean expression: A'(B'C'D' + BC'D' + BCD) + A(BC'D + BC'D + BCD + BCD' + B'C'D) I've already made a few steps to simplify it, but I'm not sure if I'm on the ...
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### When given the maxterm of function, we can find its minterm of the function, which is also the complement of the maxterm,

When given the maxterm of function, we can find the minterm of the function, which is also the complement of the maxterm. When do we use one (maxterm) instead of the others (minterm/its complement)? ...
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### Duality Principle, but confused by the example

The dual of a Boolean expression can be obtained by interchanging sums and products; also interchanging 0 and 1. But the dual of xy̅ + 1 is (x' + y) · 0 ( I think) Or the dual is (x + y) · 0. Q: do ...
1 vote
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### Need help understanding why I get the logic circuit wrong

Could someone care to explain why the logic circuit for this boolean expression doesn't look like this? When I select "build circuit," on Logisim, I get a different result:
1 vote
57 views

### Kmap and boolean equation for a function

F(A,B,C,D) = Σm(1, 2, 4, 6, 8, 10, 11, 13, 15) Here's my try of the kmap: Are my kmap and boolean equation correct for this function?
1 vote
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### How to convert SoP to NOR?

I have a logical expression: F = AB + AC + CB I know its equivalent expression via NOR: R = (A ⊽ B) ⊽ (A ⊽ C) ⊽ (C ⊽ B) It is assumed that the desired expression in NOR is unknown. I know De Morgan's ...
57 views

### Minimizing a Boolean Expression

From a 3 variable K-map I get the following expression: BC + B!C! *!=not I know that a + a!b = a, so does this mean that BC + B!C! = B + C?
1 vote
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### About DEMUX/demultiplexer: can any Boolean function be realized with the help of demultiplexers?

I know that as we OR the outputs of a DEMUX we can get a function as the first screenshot which states that an OR gate generates the one-set of the function. But can any Boolean function be realized ...
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### Where am I wrong here? I don't know why I can't get it

Question: BOOLEAN SIMPLIFICATION: Prove that F(w,x,y,z) = w’x’y’z’+w’xy’z’+ wx’y’z’+wx’y’z+ wx’yz’+w’xy’z’+ w’x’yz is equals to F(w,x,y,z) = y’z’ + wx’ My solution: F(w,x,y,z) = w’x’y’z’+w’xy’z’+ wx’y’...
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### Confusion in Duality Principle in Boolean Algebra

Maybe I have got some misconception while solving a problem. Lets a logic function, X=AB+A'C By applying duality principle, I can say that, X=(A+B)(A'+C) But I can't prove both are equal. I simplify ...
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### Implying a boolean function by using 5 NANDS only - How to implant "1" using nand?

Function: f(a,b,c,d) = b' + c' + ad + a'd' I used Karnaugh map (4x4). Received that the function is all squares except square number 7 (there it is 0). Which means: Now what is the problem? When I do ...
1 vote
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### For the 4x1 MUX shown below the Boolean Expression F(x,y,z) is [closed]

The output to a 4x1 MUX is : $Y=S_1'S_0'I_0+S_1'S_0I_1+S_1S_0'I_2+S_1S_0I_3$ My answer was : $F=A_{1}'A_{2}'x+A_{1}'A_{2}x+A_{1}A_{2}'y+A_{1}A_{2}y' \Rightarrow xyz'+xyz+y'z$ The correct answer is ...
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### A three-input NAND gate is to be used as an inverter. Which one of the following measures will achieve better results?

The two inputs not used are kept open The two inputs not used are connected to ground (0 level) The two inputs not used are connected to logic supply (1 level) None of the above I get that we can ...
1 vote
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### Show that specific functions are correct for a race-free Moore machine

Context: The goal here is to create a Latch that holds a state. We have two inputs x1, x2 and two outputs f1, f2. When (x1, x2) = (0, 1) or (x1, x2) = (1, 0) the outputs should be the same. When the ...
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### Minimizing logic expression for two-input NAND gate implementation

I have recently been struggling with this homework problem that is requiring minimization of a logic expression to be implemented using all NAND gates. The problem requires a very small number of NAND ...
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### Express state of overflow as function?

Making an ALU I want a signal that signals whenever an addition or subtraction changes the binary number from - to +. Each number u and v is 4-bits and therefore is marked by 0, 1, 2, 3 where 3 is the ...
175 views

### Why do we even need an OR gate? [duplicate]

Question This might be a naive question but hear me out, can't we just connect the two wires in parallel to build an OR gate? Like this: simulate this circuit – Schematic created using ...
1 vote
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### What is the meaning of "adding out" in Boolean algebra?

I'm having a problem with what "adding out" means. I understand that for the three first products in the second step, in the expression "(X + Y')*Z", "*Z" is replaced by ...
238 views

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### What is the maximum number of inputs to a logic gate that is being used in computing hardware these days?

I was referring to this question, but I had a confusion due to the concept of programmable logic devices. Image from UW page 7. Here the OR section can have up to 8 inputs to it. I'm confused about ...
456 views

### Confusion understanding a half adder implementation using 74153 MUX [closed]

As shown here, I have also highlighted the confusing part in the attached snapshot. In the last line of truth table, I know that sum is equal to XOR of two inputs, but here in the last line of the ...
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### If two Boolean functions $f_1$ and $f_2$ have same truth table, does that means they have exactly same characteristic? can one f1 numerate to f2?

if $f_1(x,y,z)=\neg xz+x\neg y+\neg xy\neg z+xy\neg z$ determine if $f_1$ is symmetric and whether it is unate. What I thought is: $f_1$=¬xz+x¬y+y¬z, the truth table of $f_1$ has the same ...
1 vote
2k views

### 5 Variable K-Map with Don't Cares

I stumbled upon this question and I tried doing it but my solution seemed very complicated and I wasn't sure if I grouped everything correctly or, if I did and wrote the correct expression, how to ...