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The concepts of logic gates, truth tables, and the realization of boolean formulas using sum-of-products (sop) and product-of-sums (pos) forms. It includes examples of logic gates, minimizing boolean expressions, and designing a binary full adder.
What you will learn
Typology: Study notes
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X Y Z
X Y Z 0 0 0 0 1 0 1 0 0 1 1 1
X Y
Z
X (^) Y
X Y Z 0 0 0 0 1 1 1 0 1 1 1 1
X Y 0 1 1 0
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0 0 1 0 1 1 1 0 1 1 1 0
X Y Z 0 0 1 0 1 0 1 0 0 1 1 0
X Y Z
Z
X Y
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X Y Z
Z
X Y
X Y Z 0 0 0 0 1 1 1 0 1 1 1 0
X Y Z 0 0 1 0 1 0 1 0 0 1 1 1
F
A B
C D
A B C
F
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Cin Cout
Sum Adder
A B Cin Cout Sum 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
Cout = A'BCin + AB'Cin + ABCin' + ABCin
Both Sum and Cout can be minimized.
Sum = A'B'Cin + A'BCin' + AB'Cin' + ABCin
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Before Boolean minimization Sum = A'B'Cin + A'BCin'
After Boolean minimization Sum = (A⊕B) ⊕ Cin
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Before Boolean minimization Cout = A'BCin + AB'Cin
After Boolean minimization Cout = BCin + ACin + AB
Cin Cout
Sum 1
Sum 2
0 Cin Cout
Overflow
Sum
Cin Cout
1-Bit Adder
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A B C maxterms 0 0 0 A+B+C M 0 0 1 A+B+C' M 0 1 0 A+B'+C M 0 1 1 A+B'+C' M 1 0 0 A'+B+C M 1 0 1 A'+B+C' M 1 1 0 A'+B'+C M 1 1 1 A'+B'+C' M
short-hand notation
F in canonical form: F(A,B,C) = ΠM(0,2,4) = M0 • M2 • M = (A+B+C)(A+B'+C)(A'+B+C)
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