E. T. TELECOMUNICACIONS
1BM2
DIGITAL ELECTRONICS
31/03/2008
Prof. F. J. Sànchez i Robert
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First minimum control: 30 min. Grades will be available on April, 4th
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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 ______________