{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Chapter2_1 - Chapter 2(Lect 1 Boolean Algebra Introduction...

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

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

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

View Full Document
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
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 x x’ 0 1 1 0 x y x y 0 0 0 0 1 0 1 0 0 1 1 1 x y x + y 0 0 0 0 1 1 1 0 1 1 1 1

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

View Full Document
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
DeMorgans: (x + y)’ = x’y’ Absorption: x + xy = x Postulate 4: x + yz = (x + y)(x + z)

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}