2. A logic circuit was measured in the lab and produces the following digital ou
ID: 3751321 • Letter: 2
Question
2. A logic circuit was measured in the lab and produces the following digital output function F in the time domain on the oscilloscope. Assume the higher voltages are interpreted as 1 and lower voltages as 0 a) b) c) Write the truth table for F Express this circuit as a function of its minterms written as a standard sum of products Find the minimal sum of products expression and draw the circuit that implements the expression Express this circuit as a function of its maxterms written as a standard product of sums Find the minimal product of sums expression and draw the circuit that implements the expression d) e)Explanation / Answer
(a) Truth Table
A B C F
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
(b)
A B C F
0 0 0 1 A'B'C'
0 0 1 0
0 1 0 0
0 1 1 1 A'BC
1 0 0 0
1 0 1 1 AB'C
1 1 0 0
1 1 1 1 ABC
Sum of product
= A'B'C'+A'BC+AB'C+ABC
(c) Min sum of product
Min Sum of product, F
= A'B'C'+A'BC+AB'C+ABC
=A'B'C'+BC+AC
a b c F, Output
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
Circuit will be
H L L H L H L H
(d)
A B C F
0 0 0 1
0 0 1 0 A+B+C'
0 1 0 0 A+B'+C
0 1 1 1
1 0 0 0 A'+B+C
1 0 1 1
1 1 0 0 A'+B'+C
1 1 1 1
Product of sum= (A+B+C').(A+B'+C).(A'+B+C).(A'+B'+C)
(e) Product of sum, F
F= (A+B+C').(A+B'+C).(A'+B+C).(A'+B'+C)
a b c F,Output
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
Circuit will be
H L L H L H L H
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