Boolean Algebra and Karnaugh Maps Crossword

Boolean algebra has more vocabulary in it than almost anything else in the module, and most of that vocabulary is doing real work. Commutative and associative are not decoration on a list of laws you are told to accept; they are the permissions that let you rewrite an expression at all, and knowing which one you have just used is the difference between simplifying a function and shuffling it.

This crossword covers the whole of that vocabulary in twenty terms, and it falls into four strands.

The people. Four of the answers are names, and they are worth knowing in order, because between them they are the entire history of the subject. Aristotle proposed that a statement is either true or false and there is nothing in between. Boole, more than two thousand years later, wrote down the algebra of quantities restricted to those two values, and spent the last fifteen years of his life as the first professor of mathematics at Queen’s College Cork. De Morgan gave us the two theorems about complementing a group. Shannon, in a master’s thesis, noticed that this algebra described relay and switching circuits exactly, which is the moment the subject stopped being philosophy and became engineering.

The laws. Identity, complement, commutative, associative, distributive, and the duality principle that pairs them off. The last of these is the one students most often skip and it is the most economical idea in the chapter: every valid identity has a partner obtained by swapping the operators and swapping the constants, so half the table you are asked to learn is free.

The canonical forms. Minterm and maxterm, and the sum-of-products form built from them. These are the bridge between a truth table and an expression, and they are the reason any truth table at all can be turned into a circuit without inspiration being required.

The map. Karnaugh maps, and the Gray code sequence their headers are written in. That sequence is not a stylistic choice: adjacent cells differ in exactly one variable, and that is the entire reason adjacent cells can be grouped.

How it works

Click a cell and type. Clicking the same cell again switches between across and down, and the clue you are currently in is highlighted.

Check grid marks incorrect letters in red without revealing the correct ones, so a check is a prompt to reconsider a clue rather than a way of being told the answer. Clear grid empties the puzzle. Clues can be ticked off in the list as you finish them.

Where an answer has more than one word, run the words together and leave the spaces out. Where a clue has a gap in it, the missing word is the answer and the rest of the phrase is there to tell you which one it is.

Boolean Algebra and Karnaugh Maps Crossword

Boolean Algebra & Karnaugh Maps Crossword (20 terms). Where answers have multiple words, omit spaces.

derekmolloy.ie

💡 Note:Where an answer comprises multiple words, omit the space (e.g., “The best lecturer in the world!” would be entered as DEREKMOLLOY).

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Check gridClear grid0/144 cells

Across

1.Mathematician who developed theorems regarding group complementation in Boolean algebra.(8)

3.Boolean principle stating that swapping OR/AND operators and 0/1 constants yields an equally valid equivalence.(7)

4.A mathematical statement that remains true for all possible values of its variable(s).(8)

8.English mathematician who codified algebraic rules between quantities restricted to true or false values.(5)

11.A logic ___ OR function represented by AB'+A'B that has no direct Boolean operator equivalent.(9)

13.Property allowing the order of variables in addition or multiplication to be reversed.(11)

14.MIT scholar who recognized how Boolean algebra could be applied to on-and-off relay and switching circuits.(7)

15.A sum term resulting in a 0 output for a single cell and 1s for all other cells in a truth table or map.(7)

16.The opposite logic value of a Boolean variable, denoted with an overbar or prime symbol.(10)

17.Greek philosopher who founded a bivalent system of logic based on true and false propositions.(9)

18.A visual mapping tool used to simplify digital logic functions faster and easier than Boolean algebra.(8)

Down

1.Property showing how to expand a product of a sum or factor terms out of a sum-of-products.(12)

2.A code sequence used for Karnaugh map headers where adjacent values vary by only a single binary bit.(4)

5.Property allowing groups of added or multiplied variables to be grouped with parentheses without changing the truth.(11)

6.Logical AND operation or AND-of-ORs structure where Boolean terms are joined.(11)

7.Standard Boolean form (Sum Of ___) written as a set of terms added together.(8)

9.A two-mode logic system where propositions are limited to one of two possible values.(8)

10.Type of algebra where variables are restricted to values of either 1 or 0.(7)

12.Circuit such as BCD to seven-segment that generates logic signals to drive visual displays.(7)

15.A product term resulting in a 1 output for a single cell and 0s for all other cells in a truth table or map.(7)

Where to look things up

The laws and the duality principle are in The Rules of the Game, and applying them to shrink an expression is Fewer Gates, Same Answer. The two theorems belonging to one of the names above have a demonstration of their own in Moving the Inversions. The map, its Gray-coded headers and the grouping rules are in Reading the Map, and the four-variable case in Bigger Maps and Cells That Do Not Matter.

One answer is a circuit rather than a piece of algebra, and it is there deliberately: the seven-segment decoder in Designing a Seven-Segment Decoder is where all of this stops being an exercise and becomes seven simplified functions driving a display.

If you get stuck

Leave it and come back. A clue that looks impossible often becomes obvious once a crossing answer has filled in two of its letters, and several of the longer answers here share endings, so getting one of the property names tends to give you the shape of the others.