Assignment 1 Number Representations and a 7 Segment Decoder

Number Representations and a 7 Segment Decoder
Assignment 1 
Submit two files and two files only. Do not use a zip file (or any other type of archive). Your writtenanswersshouldbeinaPDFfileandshouldhaveyournameandstudentnumberclearly indicated at the top of the document. Your circuit should have the name SevenSegDec.circ and should have your name and student number clearly indicated at the top of the document. If you write your answers by hand (probably easiest), scan your work with one of the McGill photocopiers (it will send you a pdf of the scanned document directly to your e-mail). Scanned workmustbelegible! Useadarkpenorpencilwhenpreparingyourworksuchthatyourscanned workhasgoodcontrastandiseasytoread. Allworkmustbeyourown,andmustbesubmitted usingMyCourses. Doublecheckthatyouhavecorrectlysubmittedyourassignmentasyouwill not receive marks for work incorrectly submitted.
1 NumberRepresentation,2sComplement,andFloatingPoint
Show your work in writing up answers to the following questions to get full credit. 1. Convert positional notation 0.1010112 from binary to decimal using any appropriate algorithm that was seen in class. 2. Convert positional notation 6.7510 from decimal to binary and hexadecimal using algorithms that were seen in class. 3. Convert positional notation 1FA.U06G32 from base 32 to binary and then to hexadecimal. Here, much like base 16, we use letters A through V to represent 10 through 31, and note thefractionalpartinthiscaseisUzerosixG(i.e.,itisdifficulttoseethedifferencebetween 0 and O). Use the shortcut of grouping binary bits as seen in class. 4. Convert the base 5 number 30310045 to hexadecimal. 5. Represent the base 10 number −412878610 as a 24 bit signed binary number using two’s complementformat. Convertthebinarybitpatterninyouranswertohexadecimalusing6 symbols. 6. Now that you’ve worked up an appetite for number conversions, represent -2.625 as an IEEE single precision floating point number. Give your answer in both binary and hexadecimal and show your work. Is the representation exact?
2 Seven Segment Decoder
Asevensegmentdecoderistypicallyusedtodeterminewhichlightemitting diodes in a seven segment display should illuminate to display a digit specified in binary coded decimal. Logisim includes such a seven segment display that you will use in this question. The decoder takes as input four binary bits, which we label in order from most significant bit to least significant bit, A3 A2 A1 A0. The decoder produces as output a pattern of 7 bits, S6 S5 S4 S3 S2 S1 S0, which specifies which segments should illuminate. The figure on the rightshowstherelationshipbetweenthepinsandthecorrespondingsegments of the display. Note that there is an 8th pin, S7, which controls the decimal point and that we will not use in this assignment. In this question, Instead of decoding BCD, your decoder should produce lettersAthroughJforbinarybitpatternszerothrough9,andcanproduce anyoutput(i.e.,wedon’tcare)forbinarybitpatterns10through15. Your decoder should produce exactly the patterns shown below.
1. Write out a truth table for your circuit and include this with your written answers. 2. Implementthe7booleanfunctionsintheprovidedlogisimcircuitfileusingonlyAND,OR andNOTgatesprovidedinthebuiltinlibrary(itisalsoOKtouseNANDandNORgates, and to negate inputs on gates). You may use any solution you wish, but you may find it easiest to use a sum of products approach, much like a PLA. Create your solution in the provided circuit file, as it already has a set of inputs and outputs defined. These input and output pins should not be moved so as to prevent the sub-circuit appearancefromchanging(right-mosttoolbarbuttoninlogisim)asthisisimportantfortesting. Be sure to add your name and student number in your circuit.