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E. T. TELECOMUNICACIONS 1BM2 DIGITAL ELECTRONICS 31/03/2008 Prof. F. J. Sànchez i Robert - First minimum control: 30 min. Grades will be available on April, 4th - Questions about the examination: TH:17 h – 19 h; FR: 10 h-14h VERY IMPORTANT: Draw a general schematic or plan, develop the exercise and justify the results always explaining what are you doing Minimum 2:; Designing combinational circuits using gates Fig. 1 shows the chip to be designed using logic gates, a 5-bit Gray to 7-segment display decoder to represent all the possible combinations from 00 to 31. 1 0 0 0 0 GRAY_DIGITS X4 Ta X3 Tb Tc X2 Td Te X1 Tf Tg X0 TENS R1 220 R3 220 UNITS Ua Ub Uc Ud Ue Uf Ug GRAY_DIGIT Fig. 1 Chip to be designed showing the output for the Gray combination 31 onto the common cathode displays 1. Deduce the chip’s truth table using the helping sheet in Fig. 2 2. Write the algebraic equation as a product of maxterms of the outputs Ta, Tg 3. Write the algebraic equation as a sum of minterns of the output Uc, Uf 4. Simplify by ones the output Ud using a Karnaugh map 5. Draw the logic circuit for the previously simplified output Ud using a) only NAND, and b) only NOR You can use the same exercise to study further about: 6. Simplify by zeros (POS) all the outputs using Minilog, implement the logic circuit using only NOR gates and verify it using Proteus-VSM ------------------------------ For example, for knowledge associated with minimum 3: 7. You can ask which is the power consumption of the circuit designed in (6) and which is the maximum frequency of operation if LS-TTL technology is used ------------------------------ For example, for knowledge associated with minimum 4: 8. Solve the circuit by the method of decoders and verify it in Proteus 9. Solve the function Tg by ones, and implement it by the method of multiplexers using a MUX2 Why the method of decoders is one of the best solutions to build such circuits if they have not many inputs and a lot of outputs? table 5-BIT GRAY to BCD and 7-segment CONVERTER "*********************************************** " 5-BIT GRAY to BCD and 7-segment CONVERTER "*********************************************** input X4, X3, X2, X1, X0 " 5-bit input vector for the Gray information output T1, T0, U3, U2, U1, U0 " T[3..0], U[3..0] BCD tens and units outputs (T3 = T2 = 0) " Range is 0 to 31 output Ta, Tb, Tc, Td, Te, Tf, Tg, Ua, Ub, Uc, Ud, Ue, Uf, Ug " " Truth table definition " INPUTS " BCD OUTPUTS (in Gray code) TENS UNITS digit digit " =============== ==================== =================== ==================== " X4 X3 X2 X1 X0 T1 T0 Ta Tb Tc Td Te Tf Tg Ua Ub Uc Ud Ue Uf Ug " =============== ==================== =================== ==================== U3 U2 U1 U0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 " ------------------------------------------------------------------------------------0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 " ------------------------------------------------------------------------------------1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 " ------------------------------------------------------------------------------------1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 " ------------------------------------------------------------------------------------end Fig. 2 Here you have, adapted from EX2, a helping file in Minilog format to produce the truth table for the circuit in Fig. 1 Name: ________________________________ Cooperative group: G ______________