GATE Overflow for GATE CSE - Recent questions tagged functional-completeness
https://gateoverflow.in/tag/functional-completeness
Powered by Question2Answer#boolean algebra #ex-or #functionally complete
https://gateoverflow.in/367569/%23boolean-algebra-%23ex-or-%23functionally-complete
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=2904997890548778780"></p>Digital Logichttps://gateoverflow.in/367569/%23boolean-algebra-%23ex-or-%23functionally-completeWed, 15 Dec 2021 22:58:43 +0000Partially Functional Complete
https://gateoverflow.in/282897/partially-functional-complete
In GATE, I have seen a lot of questions where we are asked to check whether a set of operations is functionally complete or not.<br />
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I know Functionally Complete and Partially Functionally Complete are two different things, but while marking answers in GATE, will we say a set is functionally complete even when it is partially functionally complete?Digital Logichttps://gateoverflow.in/282897/partially-functional-completeSun, 23 Dec 2018 03:14:28 +0000Functional Completeness Doubt
https://gateoverflow.in/265876/functional-completeness-doubt
Is Ex-NOR functionally complete? pls explain in detailsDigital Logichttps://gateoverflow.in/265876/functional-completeness-doubtFri, 16 Nov 2018 06:22:52 +0000ISI2017-PCB-CS-7-a
https://gateoverflow.in/245028/isi2017-pcb-cs-7-a
Show that $\{1,A \bar{B}\}$ is functionality complete, i.e., any Boolean function with variables $A$ and $B$ can be expressed using these two primitives.Digital Logichttps://gateoverflow.in/245028/isi2017-pcb-cs-7-aThu, 20 Sep 2018 10:17:59 +0000Functionally complete
https://gateoverflow.in/232300/functionally-complete
<p>F(x, y, z) =x + y'z' </p>
<p>It's functionally complete according to normal procedure to implement NOT & OR or AND from it. </p>
<p>But from this short trick.</p>
<p><a rel="nofollow" href="https://www.google.co.in/amp/s/www.geeksforgeeks.org/gate-gate-cs-2015-set-1-question-49/amp">https://www.google.co.in/amp/s/www.geeksforgeeks.org/gate-gate-cs-2015-set-1-question-49/amp</a></p>
<p>It's preserving 1.so it can't be functionally complete.</p>
<p>I must be wrong but I could not identify it. </p>Digital Logichttps://gateoverflow.in/232300/functionally-completeFri, 10 Aug 2018 10:11:29 +0000Functionally Complete
https://gateoverflow.in/212699/functionally-complete
Suppose a function F(A,B) = A' + B then to prove it functionally complete.Can we do it like:- <br />
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F(A,A') = A' ----> Complementation derived<br />
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F(A',B) = A + B -----> OR Operation Derived<br />
<br />
So we could conclude that its functionally Complete.<br />
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Is it the right way if not Please tell the right eay to prove the Function to be Functionally Complete.<br />
<br />
Thank You in advanceDigital Logichttps://gateoverflow.in/212699/functionally-completeWed, 18 Apr 2018 04:15:49 +0000ISRO-DEC2017-76
https://gateoverflow.in/182126/isro-dec2017-76
<p>Which of the following set of components is sufficient to implement any arbitrary Boolean function?</p>
<ol style="list-style-type:upper-alpha">
<li>$XOR$ gates, $NOT$ gates</li>
<li>$AND$ gates, $XOR$ gates and $1$</li>
<li>$2$ to $1$ multiplexer</li>
<li>Three input gates that output $(A.B)+C$ for the inputs $A, B, C$</li>
</ol>Digital Logichttps://gateoverflow.in/182126/isro-dec2017-76Sun, 17 Dec 2017 09:44:56 +0000Functionally complete sets
https://gateoverflow.in/157184/functionally-complete-sets
Which of the following set is not functionally complete?<br />
<br />
a) {XOR,1,NOT}<br />
<br />
b) {XOR,1,OR}<br />
<br />
c) {OR, NOT}<br />
<br />
d) {XOR,1, AND}Digital Logichttps://gateoverflow.in/157184/functionally-complete-setsWed, 04 Oct 2017 05:37:02 +0000Functionally Complete
https://gateoverflow.in/124558/functionally-complete
Consider the operations defined as f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(X′, Y, Z) = X′YZ + X′YZ′ + XY .<br />
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Iam following this method,<br />
<br />
A function is said to be complete if it can implement Complementation and OR logic / Complementation and AND logic.<br />
<br />
<br />
<br />
For function f(X,Y,Z) = X'YZ + XY' + Y'Z'<br />
<br />
f(X,X,X) = X'XX + XX' + X'X' = X' ( Complement logic)<br />
<br />
Now if i can implement either OR / AND logic , then can i say function is complete??<br />
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But for g(X′, Y, Z) = X′YZ + X′YZ′ + XY<br />
<br />
g(X',X',X') = XX'X' + XX'X' + X'X' = X' (Expected ans is X as X is complement of X', hence this is functionally incomplete).<br />
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<br />
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How to prove OR / AND logic is possible for f(X,Y,Z)?Digital Logichttps://gateoverflow.in/124558/functionally-completeFri, 07 Apr 2017 02:33:10 +0000GATE CSE 1989 | Question: 4-iii
https://gateoverflow.in/87883/gate-cse-1989-question-4-iii
Show that {NOR} is a functionally complete set of Boolean operations.Digital Logichttps://gateoverflow.in/87883/gate-cse-1989-question-4-iiiTue, 29 Nov 2016 19:20:42 +0000Virtual Gate Test Series: Digital Logic - Functionally Complete
https://gateoverflow.in/72520/virtual-gate-test-series-digital-logic-functionally-complete
<p> my doubt- I got first one not functionally complete but its partially complete because its use 0 for make a NOT gate please check</p>
<p><img alt="" height="392" src="https://gateoverflow.in/?qa=blob&qa_blobid=16677664031447503478" width="991"></p>Digital Logichttps://gateoverflow.in/72520/virtual-gate-test-series-digital-logic-functionally-completeSat, 08 Oct 2016 10:14:10 +0000GATE Overflow | Digital Logic | Test 1 | Question: 4
https://gateoverflow.in/68561/gate-overflow-digital-logic-test-1-question-4
<p>A set of Boolean connectives is known as functionally complete if all Boolean functions can be Synthesized using those. Which of the following sets of connectives is not functionally complete ?</p>
<ol style="list-style-type: upper-alpha;">
<li>EX-NOR</li>
<li>implication, negation</li>
<li>OR, negation</li>
<li>NAND</li>
</ol>Digital Logichttps://gateoverflow.in/68561/gate-overflow-digital-logic-test-1-question-4Mon, 19 Sep 2016 09:42:27 +0000ISRO-2013-22
https://gateoverflow.in/43845/isro-2013-22
<p>Any set of Boolean operators that is sufficient to represent all Boolean expressions is said to be complete. Which of the following is not complete ?</p>
<ol style="list-style-type:upper-alpha">
<li>{$NOT$, $OR$}</li>
<li>{$NOR$}</li>
<li>{$AND$, $OR$}</li>
<li>{$AND$, $NOT$}</li>
</ol>Digital Logichttps://gateoverflow.in/43845/isro-2013-22Tue, 26 Apr 2016 13:10:18 +0000How to prove if a boolean function is functionally complete?
https://gateoverflow.in/42522/how-to-prove-if-a-boolean-function-is-functionally-complete
Digital Logichttps://gateoverflow.in/42522/how-to-prove-if-a-boolean-function-is-functionally-completeTue, 12 Apr 2016 01:48:43 +0000GATE IT 2008 | Question: 1
https://gateoverflow.in/3222/gate-it-2008-question-1
<p>A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those. Which of the following sets of connectives is NOT functionally complete?</p>
<ol style="list-style-type:upper-alpha">
<li>EX-NOR</li>
<li>implication, negation</li>
<li>OR, negation</li>
<li>NAND</li>
</ol>Digital Logichttps://gateoverflow.in/3222/gate-it-2008-question-1Mon, 27 Oct 2014 07:38:39 +0000GATE CSE 1998 | Question: 5
https://gateoverflow.in/1696/gate-cse-1998-question-5
<p>The implication gate, shown below has two inputs ($x \text{ and }y)$; the output is 1 except when $x =1 \text{ and } y=0\text{, realize }f=\bar{x}y+x\bar{y}$ using only four implication gates.</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=10886797867086301205"></p>
<p>Show that the implication gate is functionally complete.</p>Digital Logichttps://gateoverflow.in/1696/gate-cse-1998-question-5Thu, 25 Sep 2014 19:49:21 +0000GATE CSE 1999 | Question: 2.9
https://gateoverflow.in/1487/gate-cse-1999-question-2-9
<p>Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?</p>
<ol style="list-style-type:upper-alpha">
<li>
<p>XOR gates, NOT gates</p>
</li>
<li>
<p>$2$ to $1$ multiplexers</p>
</li>
<li>
<p>AND gates, XOR gates</p>
</li>
<li>
<p>Three-input gates that output $(A.B) + C$ for the inputs $A, B$ and $C$.</p>
</li>
</ol>Digital Logichttps://gateoverflow.in/1487/gate-cse-1999-question-2-9Tue, 23 Sep 2014 18:12:08 +0000