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4.5 Don’t care entries

Note that in this case, we know that certain combinations are impossible. XY ′Z is impossible because (lv ≤ in0) ∧ (lv > in1) ⇒ (in0 > in1). Likewise, X′Y Z′ is also impossible. As a result, we can add the “don’t care” symbol in our original truth table because if an input combination is not possible, we don’t care about the output. This new truth table is represented by table 9.

XYZoutput
0 0 01
0 0 10
0 1 0?
0 1 11
1 0 00
1 0 1?
1 1 01
1 1 10

Table 9: The truth table corresponding to the merge algorithm of module 0079 with “don’t care” entries.

We can now rewrite the k-map as table 10.

Z ↓ XY →00011110
0 1 ? 1
1 1 ?

Table 10: K-map for table 6.

Next, we identify pairs of singles. There are three pairs. Let us name them {a,b,c}. We now rewrite the k-map to represent the pair ownership, represented by table 8.

The use of the “don’t care symbol can possibly help simplify the equation. This is because a question mark can be included or excluded by the groups (singles, pairs and etc.). It gives us the extra flexibility to combine groups.

Unfortunately, even the “don’t care” symbol does not help us in this example!

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