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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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Complex Boolean Algebra simplification problem [on hold]

Anyone has a solution on how to continue this simplication? \begin{align} X &= \bar R \bar S \bar T \bar u + \ldots \\ &= \bar R \bar S (\bar T\ldots)+ \ldots \end{align} Attempted but don'...
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What’s the disadvantage for solving 5 variable Kmap using overlay and reflection method? [on hold]

As far as I know solving kmap using Gray code is widely used but is there any disadvantage in it?
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Questions on types K Map [on hold]

What's the disadvantage of Overlay K Map vs the Reflection K Map and vice versa and what's the differences between these two
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3 Input XNOR gate made with XOR and not gates [duplicate]

hi i have implemented this equation with XOR and Not gate but i'm not getting the correct answers (A.B.C)+(A'.B'.C') What is the Problem ? thank you
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36 views

Finding functions for JK / D / T flip flops

I am trying to understand this concept of flip flops. Given some Karnaugh Map, all I need to know is how to find the functions of various flip-flop types: sr flip-flop (\$s = \text{ ??} \quad r = \...
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Possible ways to combine minterms from different expressions [closed]

While I understand that Karnaugh maps can be used to combine logical expressions by way of their minterms, is there any other way to do do this? So for example if I take two logical expressions \$ ...
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39 views

expressing a boolean function in another way

The following boolean expression is given: g(p,q,r) = ((p->q') -> r) Depict this boolean function only by using the operations ∧ (AND), v (OR), ¬ (NEGATION). How can I do this? I thought I could ...
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46 views

Disjunctive Normal Form

The boolean expression: y= (a'+b) * (b(c'+d')) = (a'+b) * (bc' + bd') is given. Find out the disjunctive normal form to this boolean expression. My suggestion: y= a'bc'd' + a'bc'd + a'bcd' + abc'...
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The boolean expression from a circuit

Would the final boolean expression to the circuit be right? Or do I have to multiply the brackets b(c*d)' out to bc' + bd' simulate this circuit – Schematic created using CircuitLab Edit: My ...
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logic gates, implementation [duplicate]

Task: Draw an AND circuit with 8 inputs, a circuit which implements the expression a∧b∧c∧d∧e∧f∧g∧h. Condition: Use only NOR-Gates with two inputs to solve this task. Could anyone give me a hint, ...
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Boolean algebra implementation question [closed]

We could use boolean algebra to analyse the digital circuit and use boolean simplification to optimise the circuit. In boolean expression "1 + A" is 1, whatever A is 1 or 0. But in the real digital ...
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74 views

Exclusive OR Proof

I’m given a question and its to prove exclusive OR can be the equivalent of using a NAND, OR and a AND gate show in the Boolean equation. $$A \oplus B = (A+B) \cdot (\overline{AB})$$ But when I look ...
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Mosfet switch implementation

This is the second part of the problem which I try to solve from textbook. I wrote the truth table. Z is 1 only if A, B and C are 0. I've found a boolean equation like that : \$ \large Z = \bar {A} ...
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63 views

boolean algebra question regarding how to simplify a 5 input circuit

Background: I'm teaching myself computer architecture because I do not have a technical degree and want to learn this even though my finances won't ever allow me to have a formal education. I am doing ...
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1answer
26 views

karnaugh maps simplification

I'm in the process of making a JK arbitrary sequence counter and I'm now making the k maps to get a logic equation. I was just just wondering if this is allowed (looping the bits around the middle bit)...
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1answer
42 views

Implementation of boolean function using multiplexer

Is the following question correct? Consider the Boolean expression F(A,B,C) = ABC+ AB+ AC. Implement this logic expression using one 4x1 multiplexer. Do not use C as an input to the selectors of the ...
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2answers
73 views

Is the following boolean expression correct? [closed]

The following is the logic circuit: I have to simplify the following: (((AB)')'+(B+C)+(AB)'(B+C)')C =(AB+B+C+(A'+B')(B'C'))C =(B+C+A'B'C'+B'C')C =BC+C+A'B'C+B'C =C+A'BC'+B'C
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2answers
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Implementing logic expression and the truth table of logic function

(a) Expression for \$Z\$ \$Z=(B+\overline{C})A+B(C+\overline{D})+BD\$ \$Z=AB+A\overline{C}+BC+B\overline{D}+BD\$ \$Z=AB+\overline{A}C+B\$ \$Z=B+A\overline{C}\$ (b) Truth table ...
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Checking overlow after addition of 2 integers in 2's complement form

Q) Let an−1an−2...a0 and bn−1bn−2...b0 denote the 2’s complement representation of two integers A and B respectively. Addition of A and B yields a sum S=sn−1sn−2...s0.The outgoing carry generated at ...
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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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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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37 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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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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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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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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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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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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121 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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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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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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59 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
107 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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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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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
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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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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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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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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
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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
33 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
157 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
97 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
75 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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239 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
44 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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183 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
154 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
80 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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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 ...