Question 9.PE.2: To use the multiplexer to implement a Boolean function For t...
To use the multiplexer to implement a Boolean function
For this exercise you will need the following components and equipment:
1 – 74LS153 ic (dual 4-to-1 multiplexer)
1 – +5 V dc power supply
1 – LED (5 mm) and series resistor (270 Ω)
1 Connect up the circuit of Figure 9.6, referring if necessary to Practical Exercise 9.1 for the setting-up information.
2 To implement the expression Z = Ā.\bar{B} + A.B, set the data inputs to D_0D_1D_2 D_3 = 1001. Confirm that the output Q agrees with the truth table in Figure 9.9.
3 Draw up the multiplexer truth table for the expression
Z = A.\bar{B} + Ā.B
and give the logic level for each data input.
4 Set up the necessary conditions and check the truth table by practical investigation
Conclusions
1 For the Boolean expression Z = A.B. \bar{C} +Ā. \bar{B}.C.
a) Draw up the truth table.
(b) Draw the logic diagram using AND, OR and NOT gates.
(c) Estimate the total number of ic’s required for the implementation of (b).
(Assume the following ic availability: quad 2-input AND, triple 3-input AND, quad 2-input OR, hex inverter – all in quantities as necessary.)
(d) State the logic level of each data input for implementation using a 1-of- 8 data selector.
2 Repeat the procedure of conclusion 1 for the expression
Z = A.B.C.D + Ā. \bar{B} . \bar{C} . \bar{D} + A.\bar{B}.\bar{C}.D + A.B.\bar{C}.\bar{D} + Ā.B.C.\bar{D} + Ā.B.\bar{C}.D+ Ā.\bar{B}.C.D
The requirement this time is for a 1-of-16 multiplexer.
3 As a result, state what you consider to be the advantage(s) in using a multiplexer as opposed to a number of logic gates.
