The hardware method used in Figure 9-80 can be used to generate any four-variable logic function. For example, 

is implemented by following these steps:

1. Set up a truth table in two halves, side by side as shown in Table 9-9. Notice that the left half shows all combinations of CBA when D = 0, and the right half shows all combinations of CBA when D = 1.

2. Write the value of Z for each four-bit combination when D = 0 and also when D = 1.

3. Make a column on the right side as shown, which describes what must be connected to each of the eight MUX inputs I_n.

4. For each line of this table, compare the value for Z when D = 0 with the value for Z when D = 1. Enter the appropriate information for I_n as follows:

When Z = 0 regardless of whether D = 0 or 1, THEN I_n = 0 (GND).

When Z = 1 regardless of whether D = 0 or 1, THEN I_n = 1 (VCC).

When Z = 0 when D = 0 AND Z = 1 when D = 1, THEN I_n = D.

When Z = 1 when D = 0 AND Z = 0 when D = 1, THEN I_n = D.

(a) Verify the design of Figure 9-80 using this method.

(b) Use this method to implement a function that will produce a HIGH only when the four input variables are at the same level or when the B and C variables are at different levels.

Table 9-9

Figure 9-80

Transcribed Image Text:

Z = DB CA + CBA + DCBA + CBA: