Assignment2_distributed.pdf

# The size of the interfacing decoder is ii complete

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The size of the interfacing decoder is: ii- Complete the function table of the interfacing decoder in terms of the other decoders. S 0 S S S I 0 I 0 I S 0 S I I I = Interfacing decoder address bits Output Decoders’ range 0 0 0 0 D 0-127 . MUX(0) -1 . . MUX( ) -1 I 0 ------ Output MUX( ) -1 .. . .. .

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iii- Label the lowest and highest addresses for each input and output of the following diagram. 8. Given several 4096 32 ROM chips with enables and a decoder, we can increase the memory size to 131072x32 i- How many chips are needed? ii- What is the size of the interfacing decoder? iv- Label the lowest and highest addresses for each input and output of the following diagram 9. Given the following minterm Boolean function F; F(X,Y,Z,R,S,T) = m(1,3,8,10,16, 25,35, 45,50) i- Expand the miterms in sum of product form and match it to one of the following; a- F= X`YZ`R`S`T+ X`YZ`R`ST +X`Y`ZR`S`T`+ X`Y`ZR`ST`+ X`YZ`R`S`T`+ X`YZR`S`T`+ XY`Z`R`ST + XY`ZRS`T + XYZ`R`ST` b- F= X`YZ`R`S`T+ X`YZ`RST +X`Y`ZR`S`T`+ X`Y`ZRST`+ X`YZ`R`S`T`+ X`YZR`S`T` + XY`Z`R`ST + XY`ZRS`T + XYZ`R`ST` c- F= X`YZ`R`S`T+ X`YZ`RST +X`Y`ZR`S`T`+ X`Y`ZRST`+ X`YZ`R`S`T`+ X`YZR`S`T` + XY`Z`R`ST + XY`ZRS`T + XYZRST` d- F= X`YZ`R`ST+ X`YZ`RST +X`Y`ZR`S`T`+ X`Y`ZRST`+ X`YZ`R`S`T`+ X`YZR`S`T` + XY`Z`R`ST + XY`ZRS`T + XYZRST` e- F= X`Y`Z`R`S`T+ X`Y`Z`R`ST +X`Y`ZR`S`T`+ X`Y`ZR`ST`+ X`YZ`R`S`T`+ X`YZR`S`T` + XY`Z`R`ST + XY`ZRS`T + XYZ`R`ST` f- None of the above A 0 D 0 A A D A D D = = A 0 A D 0 A A D = -- -- -- E .. . . E .. A . . A DEC DEC E .. E .. - -- --
ii- Find the decoder size needed to realize F. iii- Label all inputs and outputs of the decoder and the multiple input OR gate in the following diagram; 10. Given the following Boolean function with variables A, B, C, D, E; F= A`B`C`DE`+ A`B`C`DE + A`B`CD`E + A`B C`D`E + A`BCD`E`+ ABC`D`E`+ ABC`DE` i- Complete the truth table that includes a relation between F and the least significant variable. ii- Find the size of the most economical multiplexer that realizes F. = = = = = = = = = = = = = A B C D E F F(E) 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 = DEC 0 . . . . .. . . F

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iii- Complete the following diagram showing the values of inputs and selection variables of the multiplexer. 11- Design a combinational circuit using the most economical ROM. The circuit accepts an input x as a 3-bit number and generates an output binary number y such that y=(x+1) 2 i- How many bits needed to store the output number? ii- What is the size of the most economical ROM in bits? S 0 S 0 = = 0 1 2 . F
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• Spring '10
• DR.WEEKS
• Decimal

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