Digital Electronics Chapter 2 Boolean Algebra Logic Gates
Digital Electronics
Chapter 2 Boolean Algebra & Logic Gates
Boolean Algebra x + x' = ?
Boolean Algebra x + x' = 1
Boolean Algebra x • x' = ?
Boolean Algebra x • x' = 0
Boolean Algebra x+x=?
Boolean Algebra x+x=x
Boolean Algebra 1+y=?
Boolean Algebra 1+y=1
Boolean Algebra x+xy=?
Boolean Algebra x + x y = x (1+y) = x(1) =x
Truth Table for x + x y xy x+xy 0 0 0 1 1 1
Simplify x + x' y Hint: Make a Truth Table
Simplify x + x' y = x + y
Draw the Truth Table for x + y' z x y z x + y' z 0 0 0 ? ? ? ? ? ?
Truth Table for x + y' z x y z x + y' z 0 0 0 1 1 0 1 1 1 1 0 1 1 1
Shorthand for Truth Table (1, 4, 5, 6, 7) x y z x + y' z 0 0 0 1 1 0 1 1 1 1 0 1 1 1
Sketch the circuit for F 1 = x + y' z Hint Use AND, OR, and NOT Gates
Circuit for F 1 = x + y' z
De. Morgan’s Theorems ( x + y )' = x' y' ( x y )' = x' + y'
Was De. Morgan Right? By means of a Truth Table, verify that ( x + y )' ≠ x' + y'
Logic Gates
Logic Gates
Logic Gates
Logic Gates
From Truth Table to Boolean Write the Boolean Logic for the given function x y z F 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1
From Truth Table to Boolean F = xy'z + xyz' + xyz F = x(y'z + yz' + yz) F = x(y'z + y) F = x(z + y)
That’s All Folks!
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