# Boolean function with characters in the function value, not 0 and 1

I am currently studying the textbook Digital Design by Mano, and learned that the Boolean function can be expressed algebraically from a given truth table by forming a minterm for each combination of the variables that produces a 1 in the function and then taking the OR of all those terms.

If the following truth table was given,

x y|F          minterms
-----      ---------------
0 0|0        m_0   | x'y'
0 1|1        m_1   | x'y
1 0|0        m_2   | x y'
1 1|0        m_3   | x y


then the boolean function can be expressed as $$F=m_1+m_3=x'y+xy.$$

So far the boolean function can be equal to either 1 or 0. What if there are characters in the function value, not 0 and 1?

x y|F*
-----
0 0|a
0 1|b
1 0|c
1 1|d


My initial guess for the boolean function $$F^*$$ was $$F^*=m_0\cdot a + m_1\cdot b + m_2\cdot c + m_3\cdot d,$$ but I can't find any reference to support my assumption. Is my initial guess correct? And where do I find supporting references?

• Please do not use pictures for critical portions of your post. Pictures may not be legible, cannot be searched and are not view-able to some, such as those who use screen readers. Mar 21 at 15:13
• Hello Henrik, I just checked I can't use \begin{tabular} to create a table. What do you recommend to use? Mar 21 at 15:22
• It's been a long time since I used $\LaTeX$ a lot, so I've probably forgotten some options. But with the knowledge I still have I would probably use the array environment here. Mar 21 at 15:32
• Henriksupportsthecommunity I used GitHub-flavored markdown tables. Mar 21 at 15:39
• As the equations are nicely formatted using MathJax and you talked about \\begin{tabular} I guessed you knew $\LaTeX$/MathJax. But anything that gets rid of those pictures is an improvement. Mar 21 at 15:44