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homework_1_ece15a_2012

# homework_1_ece15a_2012 - complement numbers Perform the...

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Homework #1 due January 23 at noon Winter 2012 ECE 15a 1. Do the following conversion problems: (5p) (a) Convert decimal 37.2122 to binary. Assume that the integral and fractional parts of the number can use 8 bits each. (5p) (b) Calculate the binary equivalent of 1/7 up to 8 places. Then convert from binary to decimal. How close is the result to 1/7? 2. A computer has a word length of 8 bits, including sign. Obtain 1’s and 2’s complement of the following binary numbers: (2p) (a) 11011010 (2p) (b) 01100111 (2p) (c) 00000001 (2p) (d) 10000000 (2p) (e) 00000000 3. A computer has a word length of 16 bits, including sign. (5p) If 2’s complement is used to represent negative numbers, what range of integers can be stored in the computer? (5p) If 1 ’s complement is used to represent negative numbers, what range of integers can be stored in the computer? Express you answer in decimal. 4. A computer has a word length of 8 bits including sign. A= 10100011, B = 011010 11 are 2’s

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Unformatted text preview: complement numbers. Perform the following operations and indicate whether overflow occurs: (2p) (a) A+B (2p) (b) A-B (2p) Give the decimal values of A and B 5. A computer has a word length of 8 bits including sign. Convert decimal +61 and +24 to binary using the signed 2’s complement representation. Then perform the binary equivalent of (3p) (a) 24-61 (3p) (b) 61-24 (3p) (c) (-24)+(-61) Convert the answers back to decimal and verify that they are correct. 6. Using Venn diagrams, show that if A and B are sets, then (5p) (A’+B’)’ = AB (5p) X + XY = X (5p) 7. Suppose that a family of logic gates considers the output ranges of [0 - 0.2V] as “0” and [3.1V-3.3V] as “1”. What are the reasonable input ranges for “0” and “1”? (a) “0”: [0.1 – 0.4V], “1”: [2.3V - 3.3V]; (b) “0”: [0-0.3V], “1”: [2.8V - 3.0V]; (c) “0” : [0 - 0.5V], “1”: [2.8V-3.3V] What are the noise margins for the reasonable output ranges above?...
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homework_1_ece15a_2012 - complement numbers Perform the...

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