University:
Amherst College
Course:
COSC 111 | Introduction to Computer Science I
Academic year:

2022
Views:

300

Pages:

2
Author:

pnollobc2

Computer Systems I - Lab 2 A 4-bit incrementor For this week, we will perform a slightly different kind of arithmetic operation. This one will later be used, in Lab 3, to build a fundamentally different kind of circuit. Until then, though, this circuit has a simple definition . . . 1 An incrementor Specifically, you will design and implement a 4-bit binary incrementor. There are 16 possible integers that can be formed with 4 bits, from 0 to 15 (or, in binary, from 0000 to 1111). Given that the incrementor should add 1 to each of these possible input values, we can make a table that shows each possible input value and its corresponding output value: (original) (incremented) input value output value 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 0 Notice that when the input is at its maximum possible value (15), the output “wraps around” to the minimum possible value (0). 1 2 A suggested approach Here is a set of suggested steps that may help you both solve this problem and implement your solution as a circuit: 1. Determine the output functions: The output of your circuit should be a 4-bit number. Therefore, you have four output bits, each of whose value is determined by some Boolean logic function composed of the four inputs. Write out a truth table for the four input bits and their corresponding output bits, and then use the table to write the four output functions in disjunctive normal form. 2. Simplify the output functions: The output functions determined in the previous step are helpful, but likely more complex than necessary. Use Karnaugh maps and/or Boolean algebraic transformations to simplify those functions. 3. Draw the circuit: Draw a circuit that computes the four simplified output functions that you developed in the previous step. You may have to draw the circuit a few times to come up with a clean layout that is easy to read. 4. Build the circuit: Use the switches, LEDs, chips, and wires to implement the circuit you’ve drawn. Be sure to leave time for debugging! 3 Finishing up / Demonstrating your work Every week, there are some things you’ll have to do whether or not you’ve completed the assignment. 1. Demonstrating your work: If you’ve finished the lab, then you need to show it to the professor or the TA. You won’t get credit unless we’ve seen it work! Be sure to show both the half-adder and the full-adder. If you do not complete the lab by the end of the lab session (a likely a common occurrence), then you can show your work later in the week, before the next lab. 2. Saving your work for another day: First, be sure to label your ETS-7000; Unlabelled work may be dismantled! You need not put it away, since we lack the shelving to have everyone put theirs into storage. However, someone may reasonably move your ETS-7000 during the week. If you move someone else’s, please do so carefully. 3. Cleaning up: When you’re done, put away everything and clean up your area. That is, clean up the little bits of wire and insulation, put away the tools, etc. Leave a clean workspace, or else this lab will be a disaster before long, making it a difficult place in which to get work done. This assignment is due on Friday, September 24, at the start of the next lab session 2

Computer Systems I - Lab 2 A 4-bit Incrementor

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