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Questions tagged [boolean-algebra]

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Is this a specific logic function?

I mean it this fits a logic function or its the way its reduced only. This is the truth table \begin{array}{|c|c|c|c|} \hline A & B & C & V\\ \hline \hline \hline 0 & 0 & 0 & ...
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39 views

4 bit to 4 bit subtractor logic gates problem

I'm trying to create a 4 bit by 4 bit subtractor here but I get wrong output. In the picture it shows that 0000-1111=10001 which should be 0000-1111=11111. Please help me. By the way the rightmost IC ...
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1answer
32 views

What is the general mathematical proof that K map and Boolean Algebra are equivalent?

Is there a mathematical proof that shows K map always reduces the Boolean expression into it's minimal form?
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29 views

Will C appear in SOP when converting the minimal form AB + DB'E into canonical form?

If the minimal form contain 's 4 variables but the variables names are in random order like in the question statement the variables are A, B, D,E but C is missing . So will C come in SOP form? Someone ...
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28 views

Analysis of Sequential Circuits - Derive the state Equations from the Diagram

How can I derive boolean expression for this diagram? This is my answer: D0 = Cnt ⊕ Z D1 = ZCnt' + ZQ'Cnt + ZCntQ' For D1, I don't know what will be the expression if the input came from ...
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1answer
40 views

Is correct to apply the next boolean algebra rule?

Im trying to simplify the next boolean term \$E(A\bar{B}+C\bar{E})+\bar{E}(\bar{A}B+\bar{C}E)\$ in this way \$A\bar{B}E+CE\bar{E}+\bar{A}B\bar{E}+\bar{C}E\bar{E}\$ \$A\bar{B}E+\bar{A}B\bar{E}\$ ...
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2answers
48 views

How to simplify the next boolean algebra expresion?

Im trying to do the next simplication of the next boolean algebra term \$\bar{A}BC+A(\bar{A}C+B\bar{C})\$ In this way \$\bar{A}BC+A\bar{A}C+AB\bar{C}\$ \$\bar{A}BC+0+AB\bar{C}\$ \$B(\bar{A}C+A\bar{...
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1answer
69 views

Binary Addition 1+1 vs Boolean Operator 1 +1

Why is it that when you add two binary numbers such that 1 + 1 = 10, but when you apply the Boolean operator 1 + 1 = 1?
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1answer
59 views

Minimum number of NAND gates to implement f(x,y,z,w)=x(y+zw)+yz'

As the title states, given a function f(x,y,z,w)=x(y+zw)+yz', what are the minimum number of NAND gates you need to implement f? My first attempt at a solution was to draw a kmap to see if there was ...
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2answers
44 views

How do I express a Boolean function with don't cares (X) inputs?

I know how to minimize a Boolean function with X as outputs (using K-map). I have encountered an exercise in which I am asked to write the Normal Disjunctive Canonical Form (NDCF)/ Sum of Products (...
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1answer
37 views

Why input combinations producing output '1' constitute a standard SOP expression and those producing output '0' constitute a standard POS expression?

Why input combinations producing output '1' are picked for forming a standard SOP (Sum of Products) expression and input combinations producing output '0' are picked for forming standard POS (Product ...
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1answer
58 views

How to differentiate 01 and 10 in logic gates?

I'm looking for a device with the following truce table: The 00 and 11 case can be done with NOR and AND, but XOR can not tell 01 and 10 apart. So my questions is: Is there a device with such truce ...
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3answers
105 views

Sum-of-products, simplication

can you help to simply the following boolean expression? F = /ABC + /AB/C + ABC + AB/C + /A/BC + /A/B/C Using an online I found out the solution which should be = B + /A But I am not sure of the ...
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1answer
74 views

What is the name of this logic circuit?

Sorry for dumb question, I'm really newbie in electronic. As I wrote in topic, What's the name of this circuit? Dose the circuit has any specific name at all ?
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51 views

How to logically solve logic gates

Reading the Digital Multiplexers article on Wikipedia following is written: A 2-to-1 multiplexer has a boolean equation where A and B are the two inputs, S is the selector input, and Z is the ...
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2answers
94 views

How would I finish out this mini project (emitting 1 whenever 101 is read)?

Design a Moore finite state machine that detects 1 0 1 in consecutive digits in the input stream of 0's and 1's received every clock cycle. The circuit should output a 1 when it detects 1 0 1 ...
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2answers
51 views

Converting expression to only use NAND gates

How would I go about converting this Boolean expression so that it would only use NAND gates in its circuit? A ⋅ ¬B ⋅ ¬D + ¬A ⋅ B ⋅ ¬C ⋅ D
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1answer
70 views

There's Conflicts in the Definitions of XNOR? [duplicate]

XNOR has two definitions: \$1^{st}:XNOR=NOT(XOR)\$ \$2^{nd}: XNOR(A,B)=\overline{A}\cdot\overline{B}+A\cdot B\$ The problem is that these definitions are not equal in Odd inputs, the second ...
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1answer
67 views

How can i make f(a,b,c) = \$A \cdot B \cdot \overline C + A \cdot \overline B\cdot C\$ using only XORs and NANDs?

i have this problem where i need to make the Logical Function represented by : f(A,B,C)= \$A \cdot B \cdot \overline C + A \cdot \overline B\cdot C\ \$ using only XORs and NANDs The function was as ...
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2answers
57 views

How to transform a 3 variables Boolean Function into a K-map when some variables are not specified in the expression? [closed]

I looked at the already answered questions and used google, but I didn't found anything that explains the thing clearly. My problem is that I don't know how to solve function like ...
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1answer
49 views

How to choose which function to use depending on the parameter value? (MUX and Gates implementation)

Let's say we have A,B,C , which are all representation of decimal numbers. A and C are 4bit, B is 2bit. if A is any of those numbers (eg: 0,5,6,11 ), the function is F(A,B,C) = AB+C If A is the ...
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1answer
30 views

Creating DNF with variable in output column

I am trying to model an Arbiter in VHDL. For this I've created a Moore automaton and am currently mapping the output. The output should be when mapping from the state: ...
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1answer
118 views

How do I make a double dabble circuit with logic gates

Im attempting to make a 8 bit binary calculator that displays on multiple seven segment displays. Can double dabble be done with logic gates. If so, how?
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1answer
78 views

Make a circuit that indicates an odd number of ones using a 3-8 Demux and two logic gates

Using 3-8 Demux and two logic gates, make a circuit that received 4 bits and returns 1 if the number of 1's is odd and else returns 0. My try: Using truth table, we get that the desired function is: ...
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1answer
71 views

Karnaugh Maps in POS instead of SOP

From my understanding, to use karnaugh maps to simplify an expression, you would have an SOP expression that does not have to be canonical and then group the 1s in the table. So that got me wondering....
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1answer
153 views

J K Flip Flop and Boolean Algebra

Y=K'J'Q+K'J+KJQ' The output Y should be that of a JK flip-flop. That is: Y=JQ'+K'Q I tried to solve the following way: 1. Y=K'J'Q+K'J+KJQ' 2. =K'(J'Q+J)+KJQ' 3. =JK'+K'Q+JKQ' 4. =J(K'+KQ')+...
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1answer
35 views

WolframAlpha results for logic statement input

I was trying to simplify the following Boolean logic equation using wolframalpha.com. (not (A) and B and C) or (A and (not(B)) and C) or (A and B and not (C)) or (A and B and C) When I entered it ...
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1answer
131 views

XOR complement simplification

What is (A⊕B)' simplification? i know that : > (A⊕B)=A'B+AB' but what is the complement of that expression?
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1answer
153 views

How many logic gates are realistically feasible? [closed]

I'm actually more of a software developer and don't really know much about electrical engineering. But I do have a basic understanding of Boolean diagrams. So I had an idea for a Boolean circuit, the ...
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1answer
79 views

Implement a circuit for (a+b+c)x+(a+b+c)'x' using only OR and XNOR gates

I know XNOR is AB + A'B' so I thought the equation somehow expands to ax+bx+cx+a'x'+b'x'+c'x', but that doesn't seem right because (a+b+c)' is not the same as (a'+b'+c').
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0answers
198 views

Is it possible to build memoryless logic gates? [duplicate]

I would like to build a memoryless (possibly cyclic) logic circuit. Perhaps this is not the best name, so let me illustrate what I would like to have with an example. Consider a state machine with ...
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0answers
75 views

Boolean Algebra Equivalent

I am having a little trouble knowing what theorem to use to solve the following problem. Express the given equation without using OR gates. Hint: the expression two NANDed literals looks like this: (...
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1answer
72 views

K map minimization need confirmation

So I have to solve this f= ∑m(0,4,10,17,21,26,27,31)+ ∑d(1,5,7,8,11,16,19,20,23,24,25) Please tell me if this is correct:
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2answers
84 views

Boolean Algebra - Minimization

I have a problem with this assignment: The 26th one: I am supposed to minimize this, and I get to " XY + ZY + ( Z*(inverted X) )" But solution to this problem is I don't know how to minimize ...
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1answer
117 views

Converting boolean function (dnf) to only 2-input NANDs

I'm currently preparing for an exam and was doing some exercices regarding boolean logic. Commonly asked question is to build a function from a truth table and simplify it with a karnaugh map. After ...
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0answers
116 views

Help with Espresso optimization options

I need to minimize some boolean functions. I found in some posts here that Espresso is a great open source tool to do this. I found this link where the different optimizations options for Espresso ...
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4answers
196 views

AND Logic on 24 Volt Signals

What kind of chip and/or plug and play device could handle multi-input boolean logic with 24 volt signals? I have three sets of 20 reed Hall effect, three-wire switches that each output a 24 Volt ...
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1answer
282 views

how is this conversion possible?

I was reading Morris Mano's - Computer System Architechture and My problem is the simplification of F = AB + A'C which was: simulate this circuit – ...
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5answers
1k views

What heuristics are there (if any) to know how close a circuit is to a function?

I'm working on an AI project for circuit minimization. I'm trying to think of a heuristic to tell me how close a certain circuit is to representing a certain function. For example, if I need to ...
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1answer
112 views

Boolean law simplification

I made this exercise but I'm not sure if I made it well. q=(a+b'c)c'+a'b+ac q=ac'+b'c*c'+a'b+ac q=ac'+a'b+ac q=a(c'+c) +a'b q=a+a'b q=1 Is there someone who can ...
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1answer
201 views

De Morgan minimization

De Morgan $$y=\overline{a+\overline{b(\overline{c+d})}}+\bar{b}$$ $$y=\bar{a}(\overline{\overline{b(\overline{c+d})}})+\bar{b}$$ $$y=\bar{a}(b(\overline{c+d}))+\bar{b}$$ $$y=\bar{a}(b\overline{cd})+\...
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0answers
100 views

Is this logic gate circuit equivalent to the Simulink model?

Is this Simulink model equivalent to this circuit? Although the circuit simulated in Multisim works exactly the same as the Simulink model, switching (S1) between 5v and 0V causes an error. I guess ...
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1answer
523 views

Formulas for Carry out in a Full Adder

Given a full adder with inputs $$A, B \text{ and } C_{in}$$ The formulas for the outputs are $$S = A \oplus B \oplus C_{in} \text{ , Where } \oplus \text{means XOR}$$ and $$C_{out} = AB + AC_{in} + ...
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2answers
719 views

Build circuit from a formula

I've this formula: y = AB + AB'C + A'C I've to build a circuit with only a 2:1 mux and a OR port. I've done the truth table and k.map, but i've not idea how proced. EDIT: @jonk Thanks for your ...
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1answer
16 views

Calculating the smallest control function (conjuntive normal form)

i am trying to calculate the smallest possible control function. The function from the function table is: A = NOT(S3) & S2 & S1 v S3 & NOT(S2) & S1 v S3 & S2 & NOT(S1) v S3 &...
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1answer
225 views

Implementing a Boolean function using NOR gates with maximum 4 ports

I need to implement a Boolean function using NOR gates only. The minimized function written as PoS is: f(a, b, c, d) = (a+b)(a+c+d)(b+c+d')(a+c'+d')(a'+c'+d) I used double negation and DeMorgan's ...
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1answer
51 views

How can i simulate this circuit to match with the truth table?

How can I simulate this NAND logic circuit to match the truth table?]2
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0answers
29 views

Easiest way to get minterms from a SOP Boolean expression?

So far, I've come across problems were I need to get the list of the minterms in a truthtable from a SOP Boolean expression. For example; They way I've tackled these problems was to convert the ...
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2answers
32 views

Defined Operation Question

On my previous exam I was given 2 multiple choice questions. ...
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2answers
79 views

Karnaugh Graph Simplification

I have following truth Table : F(w,x,y,z) = Σ(0,2,5,7,8,10,12,13,14); ...