CS2630: Computer Organization Homework 3 Combinational logic and Logisim Due October 14, 2016, 11:59pm

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1 CS2630: Computer Organization Homework 3 Combinational logic and Logisim Due October 14, 2016, 11:59pm Instructions: You must submit your files to Assignments > Homework 3 on ICON. Make sure your programs assemble and run successfully, and make sure to test them on multiple inputs. The files to submit are: hw4-1.circ hw4-2.circ hw4-3.circ For each circuit file, you are responsible for following this checklist: the file name is correct inputs and outputs are labeled exactly as asked for. Labeling an input looks like this: and is different from the text tool. you ve tested your circuit as described Goals for this assignment Understand the relationship between between truth tables, boolean algebra, and logic circuits Learn to build using various digital components, like gates, shifters, and MUXs Get practice using Logisim Do this part immediately! This assignment requires the Logisim tool for creating and simulating circuits. Just as MARS was your IDE for MIPS programming, Logisim will be your IDE for digital logic.

2 Go to the resources page for directions on downloading and running Logisim ( 1. Take the Logisim tutorial Steps 0-4 at a) Build the circuit in the tutorial. b) Include labels on the inputs, as the tutorial shows in step 3. c) Save the circuit as a file called hw4-1.circ. 2. Consider the following truth table A B C Z A,B, and C are inputs. Z is the output.

3 a) Open a new circuit file and save it as hw4-2.circ. On paper, convert the truth table to a boolean expression. Put that boolean expression in your file as a text label (use ~ for NOT). b) Simplify the expression using the laws of boolean algebra Put that final boolean expression in your file as a text label. c) In the file, build your circuit in terms of AND, OR, and NOT gates. You must label the inputs and outputs A,B,C, and Z. d) Test your circuit to make sure it adheres to the truth table. You must check all 8 inputs. To do this test: click the poke tool. Using that tool, you can poke the inputs to toggle them between 0 and You will now build a 4-bit variable shifter for both shift-right-arithmetic and shift-rightlogical. Along the way, you will learn how to create subcircuits. a) Open a new circuit file and save it as hw4-3.circ. Click Project > Add circuit and for Circuit Name put right_shift_1. You ll now see that there are two circuits in your file Add a 4-bit input labeled in, a 1-bit input labeled arithmetic, and a 4-bit output labeled out. b) Build the circuit so that out is the in signal shifted to the right by one. Arithmetic should determine whether the shift is shift-right-logical (0) or shiftright-arithmetic (1). You might use the Shifting by a constant from lecture 13 as inspiration. Note that the splitter is located under wiring: You ll want to make sure that the Fan Out and Bit Width In are both set to 4:

4 c) Using the poke tool, test your circuit on both positive and negative two s complement numbers. d) Now, you will build a 4-bit variable right shifter, using right_shift_1 as a component (or subcircuit in Logisim vocabulary). Double-click main so that the magnifying glass in the explorer pane is on main circuit. Build your 4-bit variable right shifter. It should have a 4-bit input labeled in, a 2-bit input labeled shamt, and a 1-bit input labeled arithmetic (0=logical, 1=arithmetic), and a 4-bit output labeled out. To place a right_shift_1 in your main circuit, single-click right_shift_1 to highlight it, then bring your mouse over to the editing area. It should look something like this. You might use the 8-bit variable left shifter from lecture 13 as inspiration (shown below). However, mind the differences! In particular, you should use right_shift_1 to do each shift and NOT the built-in Logisim shift (box with left arrow).

5 e) Using the poked tool, test your 4-bit variable right shifter on a variety of inputs, both positive and negative, logical and arithmetic. More documentation on subcircuits is available at