1 + 1 = 1. DUH! Boolean Algebra, one of the backbones of computing. By http://www.mediotype.com - Unlock the power of math and get ready for computer wizardry.

1. Mediotype
1 + 1 = 1...Duh!
Boolean Algebra
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2. Order of operations
Please Excuse My Dear Aunt Sally
PEMDAS
Parentheses, Exponents, Multiplication,
Division, Addition, Subtraction
(4+2-1*5) + 3*2 = ?
2*2/4 = ?
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3. A Quick Word On Variables
var·i·a·ble
/ˈve(ə)rēəbəl/
Noun:
An element, feature, or factor that is liable to
vary or change.
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4. A Quick Word On Variables (cont)
Variables
In algebraic expressions, letters represent
variables. These letters are actually numbers in
disguise. In this expression, the variables are x
and y. We call these letters "variables" because
the numbers they represent can vary—that is,
we can substitute one or more numbers for the
letters in the expression.
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5. A Quick Word On Variables (cont)
Algebra
3 + x = 10
-3
-3
x = 10 - 3
x=7
It's a place holder.
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6. Questions?
diveinto@mediotype.com
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7. Basic Operations
AND x∧y = x*y
$x AND $y
$x && $y
x∧y
•
•
•
OR x∨y = x + y - x*y
x OR y
x || y
x∨y
•
•
•
NOT ¬x = 1 - x
!$x
¬x
•
•
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8. Basic Operations
AND x∧y = x*y
$x AND $y
$x && $y
x∧y
•
•
•
OR x∨y = x + y - x*y
x OR y
x || y
x∨y
•
•
•
NOT ¬x = 1 - x
!$x
¬x
•
•
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9. AND, &&, ∧
Truth table
x∧y = x*y
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10. OR, ||, ∨
Truth table
x∨y = x + y - x*y
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11. NOT, !, ¬
Truth table ... or is it
¬x = 1 - x
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12. Questions?
diveinto@mediotype.com
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13. 1.
TRUE AND TRUE = ?
2.
!TRUE || FALSE = ?
3.
(FALSE OR FALSE) AND TRUE = ?
4.
!TRUE = ?
5.
TRUE && TRUE && FALSE = ?
6.
TRUE ∧ FALSE ∨ TRUE = ?
7.
(TRUE AND TRUE) AND (TRUE OR FALSE) = ?
8.
¬FALSE ∨ FALSE = ?
Exercise
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14. Derived operations
NOR
!($x) OR $y
x → y = (¬x ∨ y)
•
•
XNOR
!(x XOR y)
x ≡ y = ¬(x ⊕ y)
•
•
XOR
$x XOR $y
x ⊕ y = (x ∨ y) ∧ ¬(x ∧ y)
•
•
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15. NOR, →
Truth table
x → y = (¬x ∨ y)
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16. XOR, ⊕
Truth table
x ⊕ y = (x ∨ y) ∧ ¬(x ∧ y)
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17. XNOR, ≡
Truth table
x ≡ y = ¬(x ⊕ y)
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18. Questions?
diveinto@mediotype.com
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19. 1.
TRUE XOR TRUE = ?
2.
¬TRUE ⊕ FALSE = ?
3.
(FALSE ∨ FALSE) ≡ TRUE = ?
4.
TRUE → FALSE = ?
5.
TRUE XOR TRUE XNOR FALSE = ?
Exercise
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