Computer Science Problems

Read each problem carefully.

1.    How many milliseconds (ms) are in one second?   _________
2.    How many microseconds (us) are in one second? _________      
3. How many bytes are in 20 megabytes? _________
4. Convert the number below from a binary number to a hexadecimal number.
1 0 0 1 1 0 1 0 1 1 0 1 1 . 0 1 1 1 1
5.    Convert the number below from a binary number to a decimal number.
1 0 0 0 0 0 0 0 1 1 0 . 0 1 1
6.    Convert the hexadecimal number below to a binary number.
8 9 A. 0 C
7. What is the decimal equivalent of the IEEE 754 binary floating point number shown below?
0 1000 0001 0110 0000 0000 0000 0000 000

For problems 8, 9 and 10, convert the following decimal numbers into 8 bit binary numbers as required for 2's complement math, and perform the indicated operations. Circle or bold your binary answer and show your work.

Notes:
Remember that positive numbers are represented in sign-magnitude format in 2's complement math

8.
+38
+30
=   

9.
+38
- 30
=

10.
- 38
+30
=

Discussion questions:

Part I - Number Conversions
Pick the amount from one of the checks in your checkbook.
1) Convert the decimal number into a binary number with three places to the right of the binary point.
2) Convert the binary number into a hexadecimal number.
3) Convert the binary number to a floating-point number using the IEEE -754 Floating-Point Standard      

Part II - Adding Binary Numbers
Select two decimal numbers between -60 and +60. One should be positive and the other should be negative.
Convert the numbers into 8-bit unsigned numbers with negative numbers in the 2’s complement form. (Remember that positive numbers have the leftmost bit =0 and negative numbers have the leftmost bit =1).
Add the two numbers together to generate an eight-bit binary result. Show your work.

Part III
If a computer is capable only of manipulating and storing integers, what difficulties present themselves? How are these difficulties overcome.

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1. The answer is 1000
2. The answer is 1000000
3. The answer is 20480...