project-1 - Preface You will need Logisim to complete this...

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Preface You will need Logisim to complete this project assignment. Further information about LogiSim is at http://www.cburch.com/logisim/ . If you have not done so already, download and install Logisim 2.7.1 from http://sourceforge.net/projects/circuit/ . 1. Introduction The objective of this project is to reinforce your understanding of binary codes, combinational logic design, and logic simulation. You must: (i) design a combinational logic circuit that displays the hexadecimal value of a gray code input according to the specifications given below; (ii) debug and test your design by simulating it using the Logisim simulator; and (iii) document your work in a short report. 2. Gray Codes Consider a system where a value is changed by being incremented or decremented by one. The value is encoded by n binary signals. As a specific example, consider a value, represented with 4 bits, being incremented from 3 to 4. In a traditional weighted binary encoding, 3 is represented as 0011 and 4 is represented as 0100. For the change from 3 to 4, three bits must change. Since the time of the transitions in the actual signals will always be different if examined at a sufficiently fine scale, the value will not change instantaneously from 3 to 4. As an example, the transition could occur as follows, where the transitions to value 7 and then value 5 are transient in nature. 0011 (3) 0111 (7) 0101 (5) 0100 (4) The physical reality of such signal transitions can create problems for applications including mechanical encoders and asynchronous (clock-free) systems.
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