SHOW YOUR WORK and WRITE NEATLY !!!
1. Perform the following conversions between bases:
a. Convert 0101 00102 to decimal:2. People are generally more comfortable using decimal rather than binary numbers, yet we often use binary numbers in computer science. There is a good reason for this, however. Very briefly explain why.
b. Convert 0011 10112 to hexadecimal:
c. Convert 3A16 to decimal:
d. Convert 19310 to binary:
e. Convert 0x19FE to binary:
(hint: recall that "0x" indicates that the number is in hexadecimal)
3. Very briefly explain the key shortcoming of the 7-bit
ASCII code which the 16-bit Unicode attempts to remedy.
4. Recalling that the ASCII code for A is 6510,
B
is 6610, C is 6710, etc, list all the
letters between A and G (inclusive) whose ASCII code, when written in binary,
has even parity. Be sure to show your work.
5. Write a circuit diagram for a 3-bit odd parity tester.
This circuit takes 3 bits of input, and has 1 bit of output, the output
being true precisely when the 3 input bits have odd parity. Be sure
to label each gate.
6. An Error Correcting Code where every value has a Hamming
Distance of at least 5 from every other value can detect 4-bit errors and
correct 2-bit errors. Very briefly explain. (Hint:
Recall that the Hamming Distance between two binary numbers is the number
of bits which must flip to convert one number into the other.)
7. True or False:
a) It is easier to convert between binary and hexadecimal numbers than to convert between binary and decimal numbers (and this is why computer scientists use hexadecimal as a shorthand for binary numbers).See Course Home Page.b) A 16-digit binary number can always be represented with a 3-digit hexadecimal number.
c) Every binary number has either even or odd parity.
d) A better name for a "clock" in a digital circuit might be a "strobe" because its primary purpose is not to tell the time of day, like a wall clock, but rather to turn on and off repeatedly like a strobe light.