Make sure to check the previous blog on K-Map Simplification as that can help a lot to have a deeper understanding. In this blog, we will learn about Don’t care conditions used while simplifying a k-map.
Sometimes there is an occasion where it doesn’t matter if the function produces 0 or 1 for a given minterm. We simply ignore the fact what the product cause it doesn’t affect the overall function. These minterms are often called as don’t care conditions and are marked as ✖ in the map.
The positive side is these don’t care conditions can be used to provide further simplification of the algebraic expression.
When working with this condition we should keep in mind that ✖’s can be 0 or 1 depending on the requirement but it need not be used at all if doesn’t contribute to the simplification of the function. The choice depends only on the simplification that can be achieved in each case.
Let us take an example with the following don’t care minterms:
F(A, B, C) = Σ (0, 2, 6) d(A, B, C) = Σ (1, 3, 5)
So, the minterms with F will produce a 1 for the K-Map. The don’t care minterms d will produce either 0 or 1, so we will denote it with ✖. The remaining minterms will produce 0. The map will look like the figure given below:
As you can see, the grouping doesn’t includes all the don’t care conditions. Only minterms 1 and 3 are included as it can simplify the expression. So, the simplified expression is:
F = A' + BC
If the don’t care conditions would not have been included with the 1’s while simplification, the simplification would have been
F = A' C' + BC'
This would have been a more complex expression requiring more gates but the expression with don’t care minterms won’t require any extra gates and is more simplified. Therefore this was chosen(expression with don’t care condition) as this expression produces the simplest Boolean Expression.
- To have a more detailed analysis of don’t care conditions click here.
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