Problem 221. Boolean algebra

Created by Tomasz

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is \"nand\":</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[nand(a,b) := ~(a&b)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your team has been developing code using the usual logical operators following MATLAB syntax:</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>~,&amp;</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:t>|. To save the project you need to write a translator that expresses MATLAB logical expressions using only the</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>nand</w:t></w:r><w:r><w:t> function.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Input</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>a</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>b</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Output</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>out: a string containing an equivalent logical expression that may only use the function</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>nand(a,b)</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example 1:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ expr = 'a|(~b)'\n =>out = 'nand(nand(a,a),b)']]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example 2:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ expr = '(a & ~a) | ~(a|b)'\n =>out = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))']]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Remarks:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>It is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>a</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>b</w:t></w:r><w:r><w:t> are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is "nand":<pre class="language-matlab">nand(a,b) := ~(a&b)
</pre>Your team has been developing code using the usual logical operators following MATLAB syntax: <tt>~,&</tt> and <tt>|</tt>. To save the project you need to write a translator that expresses MATLAB logical expressions using only the <tt>nand</tt> function.Input<ul><li>expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables <tt>a</tt> and <tt>b</tt></li></ul>Output<ul><li>out: a string containing an equivalent logical expression that may only use the function <tt>nand(a,b)</tt>.</li></ul>Example 1:<pre> expr = 'a|(~b)'
 =>out = 'nand(nand(a,a),b)'</pre>Example 2:<pre> expr = '(a & ~a) | ~(a|b)'
 =>out = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'</pre>Remarks:It is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if <tt>a</tt> and <tt>b</tt> are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.

Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is "nand":

nand(a,b) := ~(a&b)

Your team has been developing code using the usual logical operators following MATLAB syntax: |~,&| and |||. To save the project you need to write a translator that expresses MATLAB logical expressions using only the |nand| function.

Input

* expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables |a| and |b|

Output

* out: a string containing an equivalent logical expression that may only use the function |nand(a,b)|.

Example 1:

expr = 'a|(~b)'
  =>out  = 'nand(nand(a,a),b)'

Example 2:

expr = '(a & ~a) | ~(a|b)'
  =>out  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'

Remarks:

It is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if |a| and |b| are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.

Solve

Solution Stats

66 Solutions
8 Solvers

Last Solution submitted on Sep 26, 2020

Last 200 Solutions

Problem Comments

Solution Comments

Solution 25396

3 Comments

3 Comments

@bmtran (Bryant Tran) on 2 Feb 2012

Electrical Engineering Eduction FTW!

Tomasz on 2 Feb 2012

Nice! And since the eval-block, it's the only working solution for this problem so far.

@bmtran (Bryant Tran) on 6 Feb 2012

Apparently they blocked inline too now :(

Problem Recent Solvers8

Problem Tags

boolean algebra nand parser truth table

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!