PHYSICS 201 - La Salle University
|CSC 157 |Name: ________________________ |
|LAB 2 |September 6, 2001 |
Part 1. Binary and hexadecimal numbers.
All of the information stored in and processed by a computer is represented in bits (binary digits, 1's and 0's). Why?
Convert the following decimal numbers into binary and hexadecimal.
|Decimal |Binary |Hex |
|71 | | |
|43 | | |
|52 | | |
Convert the following binary numbers into decimal.
|Binary |Decimal |Hex |
|10100101 | | |
|01001010 | | |
|10111011 | | |
Part 2. A program that converts to binary form.
Add the following three statements to the main method of a program.
int num;
num=3;
System.out.println(Integer.toBinaryString(num));
Run the program. What is the output?
| |
Use the drop-down lists to find a way to do for hexadecimal what the above program does for binary.
Part 3. Negative Numbers.
Let us extend our representation to include negative numbers. Note that -13 is that number which when added to +13 gives zero. Assuming we are using eight bits to represent a number, calculate the two’s complement of 13. First replaces 1’s with 0’s and vice versa.
|0 |0 |0 |0 |1 |1 |0 |1 |
| | | | | | | | |
Next add 1 to your result.
| | | | | | | | | |
|+ |0 |0 |0 |0 |0 |0 |0 |1 |
| | | | | | | | | |
Now demonstrate that 5 + (-5) = 0
| |0 |0 |0 |0 |1 |1 |0 |1 |
|+ | | | | | | | | |
| |0 |0 |0 |0 |0 |0 |0 |0 |
Repeat the steps above to find –83. (0’s ( 1’s) Enter the binary equivalent of 83 in the first row, take the complement and place it in the second row.
| | | | | | | | |
| | | | | | | | |
And add 1.
| | | | | | | | | |
|+ |0 |0 |0 |0 |0 |0 |0 |1 |
| | | | | | | | | |
Then add 5 and –83.
| | | | | | | | | |
|+ | | | | | | | | |
| | | | | | | | | |
Does the answer make sense? How do you know?
Part 4. Negative Numbers
Set the num variable equal to –3 instead of 3 in the program in Part 2. What is the output?
| |
How many bits are being used to represent the integer?
| |
Part 5. Interpretation
Interpret the following eight-bit binary string
|1 |0 |
|B. As an signed integer | |
|C. Convert it to hex | |
Part 6. Fractions
Express the following fractions in binary form
|Decimal |Binary |
|24.875 | |
|11.625 | |
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