4. Levels of transformation The levels of transformation (refer to Patt & Patel
ID: 667629 • Letter: 4
Question
4. Levels of transformation
The levels of transformation (refer to Patt & Patel textbook Ch. 1) are often referred to as levels of abstraction. Is this a reasonable characterization? Justify your answer by providing examples or explanations.
5. Required number of bits
For each of the following, calculate the number of bits needed to uniquely represent the specified item. If you need to make any assumptions, write them down for us.
A US postal ZIP code.
A US Social Security number.
A human living on Earth. Check Worldometers for the current world population count and base your answer on that number.
6. Conversion to 2's complement
Convert the following decimal numbers into their 2's complement representation, assuming 8-bit notation. Show your work.
125
-97
7. Conversion from 2's complement
Convert the following 2's complement numbers into their decimal representation. Show your work.
10110100
01010000
8. Binary addition
Perform the following 8-bit binary arithmetic additions. Perform the operation twice: (1st) assume that the numbers are represented in unsigned binary representation, and (2nd) assume that the numbers are represented in 2's complement binary representation.
For each operation, indicate when overflow occurs. Show your work.
00101011 + 10110001
11001101 + 11011111
00111011 + 01011010
10100100 + 01001110
10100110 + 10100001
9. Binary subtraction
Perform the following 8-bit binary subtraction calculations. For all of the following problems, assume that you are executing the arithmetic operations on a computer that uses 8-bit 2's complement binary representation for its numbers. Show your work.
11001010 - 10011010
10000001 - 01100110
11001011 - 10100011
00010110 - 00100110
Explanation / Answer
this question has multiple sub parts. Please post one more question.
6)
125 will be
0111 1101
2's complement will be
1000 0010
-97 in binary will be
1001 1111
2's complement will be
0110 0000
7)
10110100
reversing it we get
0100 1011
it will be 75 in decimal
01010000
reversing it we get
1010 1111
it will be 175 in decimal.
8)
1 1
00101011
10110001
________
11011100
11111111
11001101
11011111
________
110101100
overflow will happen here.
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