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

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

Z = DB CA + CBA + DCBA + CBA:

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 In.

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 In as follows:

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

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

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

When Z = 1 when D = 0 AND Z = 0 when D = 1, THEN In = 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

DCBA 0000 0001 0010 0011 0100 0101 0110 0111 D 0 Z 0 1 0 1 0 0 1 0 DCBA 1000 1001 1010 1011 1100 1101 1110


Figure 9-80

B  So S S lo 4 12 13 74HC151 MUX N +5 V 16 17

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Digital Systems Principles And Application

ISBN: 9780134220130

12th Edition

Authors: Ronald Tocci, Neal Widmer, Gregory Moss

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