Karnaugh maps
The Karnaugh map with 2, 3 and 4 variables: Gray order, plotting a function, groups of 1, 2, 4 or 8 adjacent cells, the term of each group, the minimal expression and don't-care cases.
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- 6 topics
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Each topic is weighted the way the exam weighs it.
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A few cards from the deck
Karnaugh map: what is it?
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A truth table laid out as a grid whose rows and columns follow Gray code, so that two neighbouring cells differ by a single variable.
Neighbouring cells simplify: a·b + a·b̄ = a. The map makes those neighbourhoods visible instead of having to find them by calculation.
In a 4-variable map, rows ab and columns cd, which minterm number sits in the cell of row 11 and column 10?
14151113
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14ab = 11 and cd = 10 give abcd = 1110, that is 14. Column 10 comes fourth because of Gray order: reading its rank (3, that is 11) instead of its label would give 15.
A group of 2ᵏ cells removes … variables from its term.
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A group of 2ᵏ cells removes k variables from its term.
A group of 2 cells removes 1 variable, of 4 cells 2 variables, of 8 cells 3 variables. In a 4-variable map, a group of 8 leaves a single literal.
Gray code: what is it?
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A sequence of binary words where two consecutive words differ in exactly one bit: 00, 01, 11, 10.
The last word also differs from the first by one bit (10 and 00): the sequence closes on itself, which makes the edges adjacent.