Practice question · Put in order
Order the steps of minimising a boolean function with a Karnaugh map.
- Write the truth table of the function
- Circle groups of adjacent 1s, making every group as large as possible and a power of two in size
- Plot each 1-row of the table into its cell of the map
- Write one product term for each group, keeping only the variables that stay constant across it
- OR the terms together to get the minimised expression
Hints
- Nothing can be circled until the 1s have been placed on the map, and nothing can be placed until the function's outputs are known.
- A term is read off a group, so the grouping must be settled before any term is written.
Show the answer
- Write the truth table of the function
- Plot each 1-row of the table into its cell of the map
- Circle groups of adjacent 1s, making every group as large as possible and a power of two in size
- Write one product term for each group, keeping only the variables that stay constant across it
- OR the terms together to get the minimised expression
Why
The map is only a re-arrangement of the truth table, so the table comes first. Grouping before writing terms matters: the variables that vary within a group are exactly the ones dropped, so a different circling gives a different, possibly larger expression. Writing terms cell by cell and grouping afterwards defeats the whole method.
Practise Minimisation and Canonical Forms
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