so I am taking a summer course and the teacher is not so helpful at the moment so I was thrown the following question to do:

Derive a truth table for the following function: \$f(x,y,z)=\sum m(1,3,5,7)\$

I dont know how to interpret the equation to make the truth table which is why I am stuck. The next two questions are to derive the sum of products & products of sum of the expression \$f\$ but I think I can find that out when I get the truth table (just by learning on my own)

Also some good keywords to google about this would help.

Thank you!

  • \$\begingroup\$ Math isn't my strong suite, but what is m()? \$\endgroup\$
    – Aaron
    Jul 12, 2019 at 23:18
  • \$\begingroup\$ sum of minterms \$\endgroup\$
    – vicatcu
    Jul 12, 2019 at 23:20
  • \$\begingroup\$ @Aaron The m() is a specific set of minterms, the uppercase sigma is the symbol for a summation function. So, the combination of those two indicates a sum-of-products Boolean function. \$\endgroup\$ Jul 13, 2019 at 12:01

1 Answer 1


Write a canonical truth table with inputs x, y, z and output. Hint, it has 2^3=8 rows. Number the rows starting at zero and ending at seven. The output is one in the identified rows in the formula, and zero otherwise. If you understand the phrase "sum of minterms" you will understand why this makes sense. Look up what a minterm is, and the sum relates to Boolean algebra.

Thinking in minterms it's trivial (though not especially efficient) to implement arbitrary Boolean functions of a handful of inputs using simple multiplexers, where the inputs are select lines and the mux inputs are connected to 0 or 1 as dictated by the truth table outputs.


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