Use truth tables to show that the following two Boolean expressions are equivalent:
Simplify the following two Boolean expressions using Boolean algebra.
Simplify the following Boolean function using a Karnaugh map. Notice the don't care conditions!
The following state table is for a finite state machine with a single input x, a single output z, and two state variables A and B. Suppose two JK flip-flops are used to hold the state variables A and B. Fill in the four columns on the right of the table for the inputs JA, KA, JB, and KB to these two flip-flops.
present state | new state | ||||||||
---|---|---|---|---|---|---|---|---|---|
x | A | B | z | A | B | JA | JB | KA | KB |
0 | 0 | 0 | 1 | 1 | 0 | ||||
0 | 0 | 1 | 0 | 1 | 1 | ||||
0 | 1 | 0 | 0 | 1 | 1 | ||||
0 | 1 | 1 | 1 | 0 | 1 | ||||
1 | 0 | 0 | 0 | 1 | 0 | ||||
1 | 0 | 1 | 0 | 0 | 1 | ||||
1 | 1 | 0 | 1 | 0 | 0 | ||||
1 | 1 | 1 | 1 | 0 | 0 |
Figure 2-5 of the textbook (p. 50), shows a block diagram of a quadruple 2×1 line multiplexor. In the space below, draw a block diagram of a quadruple 4×1 multiplexor.
Now, show how a quadruple 4×1 multiplexor can be implemented with three quadruple 2×1 multiplexrs.
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