Lab 1 Problems: Data Representation and Bitwise Operations

You may NOT use any calculators.  Make sure you are on your own computer,
editing your own file.

This is your assignment for the week, not just for the day, so it is 
expected that you will not finish during this lab time.  

For each problem, make sure you write your answer on the line immediately
after the prompt.  For example:

0.) What is 2 + 2, in decimal?
0.answer)
4


---Values of Different Bases---

The following questions ask you what value a given number has
for a given number in a given base.  Write your answers in exponent
form (10^3) or a number multiplied by the exponent form (11*10^4).
Keep in mind that we start from position 0.
For example:

1.) In decimal, how much is a 1 in position 2 worth?
1.answer)
10^2


2.) In decimal, how much is a 1 in position 0 worth?
2.answer)
10^0


3.) In binary, how much is a 1 in position 3 worth?
3.answer)


4.) In hexadecimal, how much is a 1 in position 5 worth?
4.answer)


5.) In hexadecimal, how much is a 3 in position 3 worth?
5.answer)


6.) In hexadecimal, how much is a 2 in position 7 worth?
6.answer)


7.) In hexadecimal, how much is a C in position 3 worth?
7.answer)


8.) In hexadecimal, how much is a A in position 4 worth?
8.answer)



---Converting Positive decimal to Binary---

Convert the following numbers into 8-bit binary, showing all
bits.  For example:

9.) Convert decimal 0 into binary.
9.answer)
00000000


10.) Convert decimal 16 into binary.
10.answer)


11.) Convert decimal 3 into binary.
11.answer)


12.) Convert decimal 11 into binary.
12.answer)


13.) Convert decimal 66 into binary.
13.answer)



---Converting Binary to decimal---

Convert the following unsigned binary numbers into decimal.
For example:

14.) Convert binary 0000 into decimal.
14.answer)
0

15.) Convert binary 1100 into decimal.
15.answer)


16.) Convert binary 1000 into decimal.
16.answer)


17.) Convert binary 1101 into decimal.
17.answer)


18.) Convert binary 1111 into decimal.
18.answer)



---Converting decimal to Hexadecimal---

Convert the following decimal numbers into 2-digit hexadecimal
numbers, showing both digits preceded with the standard '0x'
to indicate that the number is in hexadecimal.  For example:

19.) Convert decimal 0 into hexadecimal.
19.answer)
0x00

20.) Convert decimal 15 into hexadecimal.
20.answer)


21.) Convert decimal 66 into hexadecimal.
21.answer)


22.) Convert decimal 32 into hexadecimal.
22.answer)


23.) Convert decimal 176 into hexadecimal.
23.answer)



---Bit Positions---

Remember that we number bit positions from right to left,  starting with 0.
For example:

24.) The rightmost bit of an 8-bit number is in what position?
24.answer)
0

25.) The leftmost bit of an 8-bit number is in what position?
25.answer)
7

26.) The rightmost bit of a 16-bit number is in what position?
26.answer)


27.) The leftmost bit of a 16-bit number is in what position?
27.answer)


28.) What is the 4-bit binary number that contains a 0 in all
     positions except for position 1?
28.answer)



---Bit-Level Properties---

29.) Shifting an unsigned binary number N one position to the left
     is equivalent to multipling N by what (in decimal)?
29.answer)
2

30.) Shifting an unsigned binary number N one position to the right
     is equivalent to performing truncating division (ignoring the
     remainder) by what (in decimal)?
30.answer)     
2

31.) What is the decimal result of shifting the unsigned binary
     number '0100' one position to the right?
31.answer)


32.) Shifting an unsigned binary number N four positions to the left
     is equivalent to multipling N by what (in decimal)?
32.answer)


33.) Shifting an unsigned binary number N two positions to the right
     is equivalent to performing truncating division (ignoring the
     remainder) by what (in decimal)?
33.answer)     


34.) For ANY unsigned binary number, which bit must you look at in order
     to determine if the number is odd or even?  Write your answer as
     an integer, starting from 0 (0 for bit 0, 1 for bit 1, and so on).
34.answer)



---Converting Negative decimal to Binary---

For all the below problems, your answers should have 8 bits,
and be in twos complement.  For example:

35.) What is -1 in binary?
35.answer)
11111111


36.) What is -2 in binary?
36.answer)


37.) What is -63 in binary?
37.answer)


38.) What is -12 in binary?
38.answer)



---Terminology---

You may need to use Google for these terms.

39.) How many bits are in a byte?
39.answer)


40.) How many bits are in a nibble?
40.answer)