Introduction to boolean algebra

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Information about Introduction to boolean algebra
Education

Published on February 12, 2014

Author: bugteeth

Source: slideshare.net

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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.

Mediotype 1 + 1 = 1...Duh! Boolean Algebra M

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 = ? M

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. M

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. M

A Quick Word On Variables (cont) Algebra 3 + x = 10 -3 -3 x = 10 - 3 x=7 It's a place holder. M

Questions? diveinto@mediotype.com M

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 •  •  M

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 •  •  M

AND, &&, ∧ Truth table x∧y = x*y M

OR, ||, ∨ Truth table x∨y = x + y - x*y M

NOT, !, ¬ Truth table ... or is it ¬x = 1 - x M

Questions? diveinto@mediotype.com M

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 M

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) •  •  M

NOR, → Truth table x → y = (¬x ∨ y) M

XOR, ⊕ Truth table x ⊕ y = (x ∨ y) ∧ ¬(x ∧ y) M

XNOR, ≡ Truth table x ≡ y = ¬(x ⊕ y) M

Questions? diveinto@mediotype.com M

1.  TRUE XOR TRUE = ? 2.  ¬TRUE ⊕ FALSE = ? 3.  (FALSE ∨ FALSE) ≡ TRUE = ? 4.  TRUE → FALSE = ? 5.  TRUE XOR TRUE XNOR FALSE = ? Exercise M

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