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4.4 Another example

In module 0079, the “Merge” algorithm has a look up table based on comparison results. For simplicity, let X = lv ≤ in0, Y = lv ≤ in1, Z = in0 ≤ in1. Then, table 6 represents the truth table.

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

Table 6: The truth table corresponding to the merge algorithm of module 0079.

We can rewrite the truth table as a k-map as in table 7.

Z ↓ XY →00011110
0 1 1 1
1 1

Table 7: 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.

Z ↓ XY →00 01 11 10
0 1 {a}1{a,b,c}1 {b}
1 1 {c}

Table 8: K-map for table 6 with pair ownership.

In this case, we have to select all the pairs, which means the result is W = X′Z′(a) + Y Z′(b) + X′Y (c).

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