Goals:
• Get you familiar with data representation and simple logic operations for this course.
Requirements:
• Finish the questions section below. Points for each question included in parenthesis.
• Show your work to get full credit. ZERO point without steps for a result.
Deliverables:
• Save your solutions of questions as a pdf document. You can use this document as worksheet.
• Name document as a “Firstname_Lastname.pdf”.
• Submit your “Firstname_Lastname.pdf” through the Canvas system. You do not need to submit hard copies.
Rebuttal period:
Questions:
1. (9 points) Convert the following unsigned base 2 numbers (binary) to base 16 numbers (hexadecimal):
A. 0110 0001 1111
B. 1000 1111 1100
C. 0001 0110 0100 0101
2. (27 points) Convert the following binary numbers to base 10 numbers (decimal). Each time if binary numbers are represented in:
a) Signed magnitude representation.
1) 1100 1010 =
2) 1111 0010 =
3) 1000 0111 =
b) One’s complement representation.
1) 1100 1010 =
2) 1111 0010 =
3) 1000 0111 =
c) Two’s complement representation.
1) 1100 1010 =
2) 1111 0010 =
3) 1000 0111 =
For example, question A, if 1100 1010 is a binary number represented in signed magnitude representation, what is the decimal value? Also do it again if 1100 1010 is a binary number in one’s complement representation and two’s complement representation. There are 9 separate answers in total.
3. (36 points) Convert the following base 10 (decimal) values to binary numbers (8-bits). Each binary result represented in:
a) Signed magnitude representation.
1) -100d =
2) -16d =
3) -21d = 4) -0d =
b) One’s complement representation.
1) -100d =
2) -16d =
3) -21d =
4) -0d =
c) Two’s complement representation.
1) -100d =
2) -16d =
3) -21d =
4) -0d =
(There are 12 separate answers in total.)
4. (4 points) What is the range of: A. An unsigned 7-bit number?
B. A signed 7-bit number?
5. (12 points) Solve following bitwise operations (∧ = AND, ∨ = OR)
e.g. 0101 ∧ 0011 = 0001
1. 1000 ∧ 1110
2. 1000 ∨ 1110
3. (1000 ∧ 1110) ∨ (1001 ∧ 1110)
6. (9 points) Please demonstrate each step in the calculation of the arithmetic operation 25 - 65. (both 25 and 65 are signed decimal numbers)
7. (3 points) Mathematically the answer in Q6 is -40d. Please verify your answer in Q6 using a conversion of 2’s and decimal numbers.
