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The solutions to quiz 1 and quiz 2 for cs 150 - spring 1990 at the university of california, berkeley. The quiz covers topics such as sequential networks, state tables, and binary multiplication using j-k flip-flops and full adders.
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BERKELEY • DAVIS • IRVINE • LOS ANGELES • RIVERSIDE • SAN DIEGO • SAN FRANCISCO SANTA BARBARA • SANTA CRUZ Department of Electrical Engineering and Computer Sciences
CS 150 - Spring 1990 Prof. A. R. Newton
Room 100 Lewis, Thursday 4/ (Open Wakerly, Calculators OK, 1hr 20min)
Include all final answers in locations indicated on these pages. Use reverse side of sheets for all working. If necessary, attach additional sheets by staple at the end. BE SURE TO WRITE YOUR NAME ON EVERY SHEET.
(1) A sequential network has one input and one output. The output becomes 1 and remains 1 thereafter when at least two zeros and at least two ones have occurred as inputs, regardless of the order of occurrence. Draw a state graph (Moore type) for the network (9 states are sufficient). Your final state graph should be neatly drawn with no crossed lines.
(additional space for working, Problem 1)
(additional space for working, Problem 2)
(3) Design a parallel binary multiplier which multiplies two 3-bit binary numbers to for a 6-bit product. This multiplier is to be a combinational network consisting of an array of 1-bit full adders and AND gates only (no flip-flops).
(a) Show a schematic diagram.( Hint: The AND gates can be used to multiply by 0 or 1 and the full adders can be used to add 2 bits plus a carry. Six full adders are required.)
(b) Demonstrate you multiplier works by showing the values on all internal outputs (outputs of adders and outputs of AND gates) when multiplying 111 by 111.
(c) Using exactly 5 bits, express the following numbers in 2's-complement form:
(a) 12 = __ __ __ __ __
(c) 31 = __ __ __ __ __