Design a Single-Output Combinational Switching Circuit Minterm ...

F
' '
' '
= ABC D + A BCD + ABC D
1101
= ∑ ( 7,
12 , 13 )
0101
0111
1001
1100
'
' '
'
'
P = ( A+
B + C + D )( A + B + C + D )( A+
B + C + D)
0010
= ∏(
2,
5,
9)
EX:
Given
Q(
A,
B,
C,
D)
= ∑(
0,
1,
7,
8,
10,
11,
12,
15)
Note: Q is four variable function and there will be 2 4
= 16 combinations whose decimal values range from
0 to 15. It has 8 minterms and should have 16-8=8 16 8=8
maxterms
Q(
A,
B,
C,
D)
= ∏(
2,
3,
4,
5,
6,
9,
13,
14)
Incompletely Specified Function
Truth Table with Don't Cares which are indicated
by X in the output
Case 2: We do not care
whether it is 0 or 1 for certain
input combination.
F = ∑ m(
0,
3,
7)
+ ∑ d(
1,
6)
F = ∏ M ( 2,
4,
5)
• ∏(
1,
6)
It is desirable to choose values
for the don’t care terms which
will help simplify the function!
X Y Cin Cout Sum
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
Truth Table for a Full Adder
Incompletely Specified Function
First Case: Assume that the output of N1 does not
generate all possible combinations of values for A,
B, and C. This will lead to the incompletely
specified function for N2 since certain combination
of circuit inputs did not occur.
Examples of Truth Table
Construction
•Example 1
•Example 2
•Example 3
•Example 4
On Pages 94-97.
Truth Table for Binary Full Subtracter