cosc3330-hw1-sol - COSC 3330 Computer Architecture College...

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COSC 3330 - Computer Architecture College of Natural Sciences and Mathematics Spring 2011 Due: Feb 8, 2011 Student ID (last four digits): ________________________ Name: ________________ 1. (12 points) Determine the numbers for all the question marks (?) shown in the following equations. Note that all these numbers are “signed” numbers (with sign extension) and are represented by two’s complement using 2 bytes (16 bits). Please show how you derive your answers step-by-step. You will not receive any credit if you only write down your answers with no derivation. 1.1. (-177) 10 = (?) 16 177 = 0000, 0000, 1011, 0001 -177 = 1111,1111, 0100, 1110 + 1 = 1111, 1111, 0100, 1111 FF4F 1.2. (CFAF) 16 = (?) 10 (1100,1111,1010,1111) 0011, 0000, 0101, 0000 + 1 = 0011, 0000, 0101, 0001 = - 12369 1.3. (1010 0011 0110 0011) 2 = (?) 16 A363 1.4. (139) 10 = (?) 7 139 = 2*7^2 + 5*7^1 + 6* 7^0 = 256 2. (20 points) Consider the following logic circuit:
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2.1) Write the Boolean equation that expresses the output of this circuit in terms of the three inputs, A, B, and CLK (3 points). __________________ _______ ____ A*CLK * (B + CLK) 2.2) Apply De Morgan’s theorem to the Boolean equation from 2.1 (4 points). __________________ _______ ____ A*CLK * (B + CLK) ________ ____ = (A*CLK) + (B + CLK) ___ = (A*CLK)+ (B * CLK) __ = CLK(A + B) __ = CLKA + CLKB 2.3) Write a truth table of the above circuit (3 points).
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