Description
Goals:
- Get you familiar with data representation and simple logic operations for this course
Questions:
- (9 points) Convert the following unsigned base 2 numbers (binary) to base 16 numbers (hexadecimal):
- 0110 0001 1111
- 1000 1111 1100
- 0001 0110 0100 0101
- (27 points)
(2.1) Convert the following binary
- 1100 1010
- 1111 0010
- 1000 0111
numbers into base 10 numbers (decimal), binary numbers are represented in signed magnitude representation.
- Redo the question 2.1, if the binary number are represented in One’s complement representation.
- Redo the question 2.1, if the binary number are represented in Two’s complement representation.
For example, question (2.1), 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 9 questions in total.
- (36 points, answer 12 questions in total.)
(3.1) Convert the following base 10 (decimal) values to binary numbers (8-bits): a. -100d
- -16d
- -21d
- -0d
Each binary result represented in Signed magnitude representation.
- Redo the question (3.1), convert binary into in One’s complement representation.
- Redo the question (3.1), convert binary into in Two’s complement representation.
- (4 points) What is the range of: A. An unsigned 7-bit number?
- A signed 7-bit number?
- (12 points) Provide the answer to the following problems (∧ = AND, ∨ = OR)
- 1000 ∧ 1110
- 1000∨1110
- (1000∧1110) ∨ (1001∧1110)
- (9 points) Please demonstrate each step in the calculation of the arithmetic operation 25 – 65. (both 25 and 65 are signed decimal numbers)
- (3 points) Mathematically the answer in Q6 is -40d. Please verify your answer in Q6 using a conversion of 2’s and decimal numbers.
