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Unformatted text preview: NOT: • out = ā = !a = a AND: • out = a ∙ b = a & b = a b OR: • out = a + b = a  b = a b XOR: • out = a b = ab + āb Logic Equations • Constants: true = 1, false = 0
• Variables: a, b, out, …
• Operators (above): AND, OR, NOT, etc. NOT: • out = ā = !a = a AND: NAND: OR: NOR: XOR: XNOR: • out = a ∙ b = a & b = a b
• out = a + b = a  b = a b
• out = a b = ab + āb Logic Equations • out = a ∙ b = !(a & b) = (a b) • out = a b = !(a  b) = (a b) • out = a b = ab + ab • Constants: true = 1, false = 0
• Variables: a, b, out, …
• Operators (above): AND, OR, NOT, etc.
•. Identities useful for manipulating logic equations
– For optimization & ease of implementation a + 0 = a + 1 = a + ā = a 1
1 a ∙ 0 = a ∙ 1 = a
a ∙ ā = 0
0 Identities useful for manipulating logic equations
– For optimization & ease of implementation = = a + a b = a(b+c) = = • functions: gates ↔ truth tables ↔ equations
• Example: (a+b)(a+c) = a + bc
a b c 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Binary (two symbols: true and false) is the basis of Logic Design
More than one Logic Circuit can implement same Logic function. Use Algebra (Identities) or Truth Tables to show equivalence. From Switches to Logic Gat...
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This document was uploaded on 02/22/2014 for the course CS 3410 at Cornell University (Engineering School).
 Spring '08
 KAVITABALA
 Computer Science, Computer Architecture

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