1. An analog voltage is in the range of 0-5V. If it can be measured with an accu

Question

1. An analog voltage is in the range of 0-5V. If it can be measured with an accuracy of + -50mv, at most how many bits of information is conveyed?

2. The babylonians developed the sexagesimal(base 60) number system about 4000 years ago. How many bits of information is conveyed with one sexigesimal digit? How do you write the number 4000base10 in sexigesimal.

3. A classroom has an old clock on the wall whose minute hand broke off. a.) If you can read the hour hand to the nearest 15 minutes, how many bits of information does the clock convey about time? b.) If you know whether it is before or afternoon, how many additional bits of information do you know about the time?

Explanation / Answer

2)

The easiest way to convert from base 10 to a foreign base is to divide repeatedly by the foreign base. On each division, set aside the remainder and continue to divide the quotient by the base until you reach a quotient of zero. The remainders will be the digits of your foreign-base number, with the least significant bit being the remainder you first got.

4000/60 = 66 remainder (40) e

66/60 = 1 remainder 6

1/60 = 0 remainder 1

so the answer is 16e

3600 values, or 12 bits of information

3)(a) The hour hand can be resolved to 12 * 4 = 48 positions, which represents log248 = 5.58 bits of information.

(b) Knowing whether it is before or after noon adds one more bit

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