Chapter2_1 - Chapter 2 (Lect 1) Boolean Algebra...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 2 (Lect 1) Boolean Algebra Introduction Two-Valued Boolean Algebra Elements and Operators Postulates and Theorems Boolean Functions Truth Tables Circuits Application Canonical and Standard Forms Minterms and Maxterms
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Boolean Algebra The algebra of two values (in this course) Used in mathematical methods to simplify logic circuits Simpler circuits leads to Reduced complexity Reduced component count Reduced circuit size Bottom line reduced cost = higher profits
Background image of page 2
Defined on a set of two elements {0,1} Two binary operators + and The complement operation We will apply to gate-type circuits Operator Rules Two-Valued Boolean Algebra xx 01 10 x y x y 0 00 0 0 1 11 x y x + y 0 0 1 1
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Postulates and Theorems Table 2.1 P2 x + 0 = x x · 1 = x P5 x + x’ = 1 x · x’ = 0 T1 x + x = x x · x = x T2 x + 1 = 1 x · 0 = 0 T3 (x’)’ = x P3 x + y = y + x xy = yx T4 x + (y + z) = (x + y) + z x(yz) = (xy)z P4 x(y + z) = xy + xz x + yz = (x + y)(x + z) T5 DeMorgan (x + y)’ = x’y’ (xy)’ = x’ + y’ T6 Absorption x + xy = x x(x + y) = x
Background image of page 4
DeMorgans: (x + y)’ = x’y’ Absorption: x + xy = x Postulate 4: x + yz = (x + y)(x + z)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/15/2011 for the course E 202 taught by Professor Staff during the Fall '11 term at University of Alabama - Huntsville.

Page1 / 15

Chapter2_1 - Chapter 2 (Lect 1) Boolean Algebra...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online