Chapter 4: Q8E (page 304)
Suppose that the cipher text, DVECFMV KF NFEUVI, REUYRK ZJKYV JVVUFW JTZVETV. was produced by encrypting a plain text message using a shift cipher. What is the original plain text.
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The odometer on a car goes to up miles. The present owner of a car bought it when the odometer read miles. He now wants to sell it; when you examine the car for possible purchase, you notice that the odometer reads miles. What can you conclude about how many miles he drove the car, assuming that the odometer always worked correctly?
Convert each of the integers in Exercise 6 from a binary expansion to a hexadecimal expansion.
a) (1111 0111)2
b) (1010 1010 1010)2
c) (111 0111 0111 0111)2
d) (1010 1010 1010 101)2
Answer Exercise 36 for two's complement expansions.
36. If m is a positive integer less thanhow is the one's complement representation of -m obtained from the one's complement of m, when bit strings of length n are used?
Show that the binary expansion of a positive integer can be obtained from its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.
33. Show that a positive integer is divisible by 3 if and only if the difference of the sum of its binary digits in even numbered positions and the sum of its binary digits in odd-numbered positions is divisible by 3.
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