What should be the dimensions of a 3-variable K-map? A 4-variable K-map?
3 var - 2 x 4
4 var - 4 x 4
What is Gray code?
ordering of the binary numeral system such that two successive values differ in only one bit
Given the variables A and B, classify the following K-map labels as valid or invalid Gray code:
A'B, A'B', AB', AB valid
A’B’, A’B, AB’, AB invalid
AB’, A’B’, A’B, AB valid
AB, AB’, A’B, A’B’ invalid
AB, AB’, A’B’, A’B valid
A'B', AB, A'B, AB' invalid
A'B, AB, AB', AB valid
A'B', A'B, AB, AB' valid
Practice translating truth tables into K-maps
K-map groupings
What are the restrictions on K-map groupings?
Groups must be rectangular (but they may wrap around edges!)
Groups may only contain “1s” or “Xs”
All “1s” must be contained within at least one group
Groups must be as large as possible
The size of a group must be a power of 2 - note that you may have a group of size 1
What do you do with don’t-care values when making your K-map groupings?
mark spots with Xs, and can use them if needed
can use as either a 1 or 0 or ignore entirely
Practice 3-variable and 4-variable K-map groupings
Practice converting groupings into a sum-of-products expression
We've put together a spreadsheet of 4-variable K-map grouping for practice. You can find the spreadsheet here.
The cells filled with black contain the solutions to the minimal groupings as sum-of-products expressions. To view a solution, click on the filled-in cell; you'll be able to see the contents of the cell in the formula bar above.
