D o = A B C D 1 = A B C D 2 = A B C D 3 = A B C D 4 = A B C D 5 = A B C D 6 = A B C D 7 = A B C A B C
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1 C23 Homework #6: Building Blocks Homework and Solution. (2 points) Design a 3-to-8 using only NAND gates and inverters. A B C D o = A B C D = A B C = A B C D 3 = A B C D 4 = A B C D 5 = A B C D 6 = A B C D 7 = A B C
2 2. ( points) Construct a 4-to-6 with an enable input using five line s with enable inputs. Inputs A A A 2 A 3 A A D D D 3 A 2 A D 4 D 5 D 6 D D 8 D 9 D D D 3 D 4 D 5
3 3. (5 points) Design a 4-to- MUX using AND gates and inverters. Remembering the Boolean identities X*=X, X*=, X+= and X+=X should be useful in your design process. S S D o S S D D D S S S S D 3 D 3 S S
4 4. (2 points) Design a 4-to-2 priority encoder with NOR gates and inverters such that the inputs D, D, D2, and D3 have the following priorities: D>D>D2>D3 Using the design methodology in class with this different priority these new boolean equations were derived. The circuit uses mied logic notation to illustrate the implementation with NOR gates. Condensed Truth Table Describing Priority ncoder with D>D>D2>D3 D 3 D D A A V D D D 3 A = D D D D D 3 A = D + D A = D + D A = D D V= D +D + +D 3 D A D D D A D D D 3 V
5 5. (2points) Assume that you are a cosmonaut on the Mir space station. All of a sudden a solar flare causes a power surge that destroys a 4-to-6 in one of your control panels. You can pinpoint the defective chip because it is the only chip that has smoke coming out of it!! Due to cut backs in the Mir budget, all you find in your toolbo is a 4- to- MUX, 8-to- MUX, and a 4-to-2 priority encoder. First, which of these parts (only use ON of them) could you use to replace the (and the OR gate) in the following circuit such that the output performs the same function. Second, show the design with the new replacement part. (Assume that you also have as many inverters as you need) At first you might consider the problem and say, Hey I will quickly put in an 8-to- MUX to implement the function implemented by the and the OR gate. You could draw up a truth table that looks something like this: Brown Brown = =
6 From the truth table, you could hook up an 8-to- MUX according to the following schematic: 8-to- MUX S 2 S S Brown Black After a little more consideration, you might realize that the brown line is not actually needed. This can be verified by trying to simplify the output using a K-MAP as follows: Bl Y Br G F= * + *
7 This K-map clearly shows that the brown line is not needed and reveals that the designer of the original control panel on MIR did not have an optimal design. Therefore, you decide to now use a 4-to- MUX to implement the function and save your 8-to- MUX for more comple tasks! The implementation with a 4-to- MUX is given by: = GRD 4-to- MUX Black 2 3 S S
8 6. (5 points)you decide that you are going to build your own digital calculator. The first thing that you must do is design the keypad input. When a button on your keypad is pressed, a high voltage is sent along the corresponding wire to your digital circuit. ach keypad button provides an input into the digital circuit that you are going to design. Assume that each key type is encoded with a 4 bit code according to the following convention: key key =; 2 key =, 3 key = ; 4 key = ; 5 key = ; 6 key = ; 7 key = ; 8 key =; 9 key = ; + key =; - key =; * key =; / key =; = key =; clear key =. Do you need a 4-to- MUX, 6-to- MUX, -to-6 DMUX, 3-to-8, 6-to-4 encoder, 4-to-6, 6-to-4 priority encoder, or an 8-to-3 encoder to produce these codes from the basic keypad description. Once you pick one of these choices, show how you would hook up the component to your keypad. Use the following names for the keypad signals: key, 2key, 3key, 4key, 5key, 6key, 7key, 8key, 9key, pluskey, minuskey, *key, /key, =key, clearkey. key key 2key 3key 4key 5key 6key 7key 8key 9key pluskey minuskey *key /key =key clearkey to-4 priority encoder V A A A 2 A 3 key-pressed Really a priority encoder is needed so that we can handle the condition when no key is selected in which V (which I have label key-pressed) will be a zero!!!
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