# Assignment 3: logic

5 March 2019

## Truth table

Write a complete truth table for all values of the Boolean expression assigned to you in the table below. (If you are not in this list, contact me to obtain your expression.)

Remember the correct order of operations: parentheses `()`, followed by negation (NOT `'`), then AND `·`, then OR `+`, and finally XOR `⊕`. Every expression here uses exactly three variables, so your table should have eight rows. You may create your truth table on paper and then take a very clear picture of it, or do it directly in a document or spreadsheet file.

ID Initials Expression
100535952 AG `(B'⊕B)·(A+C)'`
100551455 AM `A'+C⊕C'·B`
100588155 BM `(C·A)'+(B'⊕C)`
100585354 CF `B·A⊕(C+A')'`
100620003 CT `A'·C+(A⊕B)'`
100580521 DD `(B⊕C)'+B'·A`
100504153 EC `A+B⊕(C·B')'`
100538993 JM `C'·A+(B⊕A)'`
100567397 JM `B·A'⊕C'+B`
100610792 KB `(C⊕B)·(C'+A)'`
100589498 KK `(B⊕C)'·(B'+A)`
100367370 KS `B'+C⊕C'·A`
100515931 ML `B·C'⊕A'+A`
100629088 SA `(B+A)'·(B⊕C')`
100632069 SB `C'·B⊕A+A'`
100625271 SF `B·A'⊕A+C'`
100579463 SK `(A'+C)'·(B⊕C)`
100551483 SL `B+B'⊕C·A'`
100619272 SM `(B'+C)'·(B⊕A)`
100580414 SQ `(B⊕A')+(C·A)'`
100586641 ST `A'+A⊕C'·B`
100594503 SW `(C'·A)'⊕B+A`
100555030 XL `B+C⊕(C'·A)'`

## Circuit

Using Logisim, implement a circuit for your assigned Boolean expression. It should have exactly three two-state input pins, labeled as `A`, `B`, and `C`. It should have one output pin or LED. Test the circuit against your truth table to verify the results. If you find a way to implement exactly the same calculation with fewer gates, that’s fine (but not necessary). Save your work as `truth1.circ` and attach that file to the Wiki to submit.

## How to submit

As before, go to your cs101 project page on `gitlab.liu.edu` and select Wiki in the sidebar. Push the green New page button. Set the “Page slug” (title) to exactly `A3` (capital `A`, the number `3`, no spaces). Attach the truth table (an image or office document) and the Logisim circuit file using the Attach a file button, then save the page.