HW05 Digital Logic
================================================================================
You can find the questions at the end of Chapter 3 of the textbook.
1. Analog circuits are subject to noise that can distort their output. Are digital circuits immune to noise? Discuss your answer.
2. A logician drives into a drive-in restaurant and says, ‘‘I want a hamburger or a hot dog and french fries.’’ Unfortunately, the cook flunked out of sixth grade and does not know (or care) whether ‘‘and’’ has precedence over ‘‘or.’’ As far as he is concerned, one interpretation is as good as the other. Which of the following cases are valid interpretations of the order? (Not that in English ‘‘or’’ means ‘‘exclusive or.’’)
a. Just a hamburger.
b. Just a hot dog.
c. Just french fries.
d. A hot dog and french fries.
e. A hamburger and french fries.
f. A hot dog and a hamburger.
g. All three.
h. Nothing—the logician goes hungry for being a wiseguy.
3. A missionary lost in Southern California stops at a fork in the road. He knows that two motorcycle gangs inhabit the area, one of which always tells the truth and one of which always lies. He wants to know which road leads to Disneyland. What question should he ask?
4. Use a truth table to show that X = (X AND Y) OR (X AND NOT Y).
5. There exist four Boolean functions of a single variable and 16 functions of two variables. How many functions of three variables are there? Of n variables?
6. There exist four Boolean functions of a single variable and 16 functions of two variables. How many functions of four variables are there?
7. Show how the AND function can be constructed from two NAND gates.
17. A 16-bit ALU is built up of 16 1-bit ALUs, each one having an add time of 10 nsec. If there is an additional 1-nsec delay for propagation from one ALU to the next, how long does it take for the result of a 16-bit add to appear?
30. Multicore chips, with multiple CPUs on the same die, are becoming popular. What advantages do they have over a system consisting of multiple PCs connected by Ethernet?
31. Why have multicore chips suddenly appeared? Are there technological factors that have paved the way? Does Moore’s law play a role here?
32. What is the difference between the memory bus and the PCI bus?