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 = 01101011 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 2s 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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This note was uploaded on 01/25/2012 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.

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homework_1_ece15a_2012 - complement numbers. Perform the...

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