Lec5_BooleanAlgebra_11_updated

Lec5_BooleanAlgebra_11_updated - 1 Lecture 5 Boolean...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: 1 Lecture 5 Boolean Algebra and Digital Logic 2 Boolean Algebra Boolean Algebra Boolean Algebra Boolean Algebra • Boolean algebra: The theoretical basis used in the analysis and design of electronic digital circuits. • It provides the operations and the rules for working with the set {0,1} – electronic and optical switches can be studied using this set and the rules. • The operation of a circuit is defined by a Boolean function that specified the value of an output for each set of inputs. • The first step in constructing a circuit is to represent its Boolean function by an expression built up using the basic operations of Boolean algebra . — Boolean algebra makes use of variables and operations. — A variable take on that 1 : TRUE 0 : FALSE For example D = B + ( Ā · C) If B is 1 or if both A = 0 and C =1, D is equal to 1 — Basic Operations ( Notation) AND : A AND B = A · B = A ^ B OR : A OR B = A + B = A v B NOT : NOT A = Ā = A ’ 3 Gate Gate Gate Gate-Level Concepts Level Concepts Level Concepts Level Concepts • Switch circuits — All switches have binary input/output signals and two states: open and closed (corresponding to 1 and 0). • Logic gates: constructed using switch circuits — NOT (Inverter) — AND and OR gates — NAND and NOR gates — EXCLUSIVE-OR a nd NOR-gates • All operations including arithmetic and logic are implemented along with the above basic logical functions and their combinational circuitry in ALU. — Three main ways to represent logic gate 1. symbolic representation 2. logical expression: z = f ( X ) = f ( x1, x2, ..., xn ) 3. truth table: n variables → 2 n different cases 4 Gate Gate Gate Gate-Level Concepts Level Concepts Level Concepts Level Concepts 1-bit half adder • Example: half adder adds two binary digits to form Sum and Carry A B 0 0 1 1 0 1 0 1 Sum Carry 0 1 1 0 0 0 0 1 A + B ? C ? S 5 Boolean Algebra 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 F C B A Logic Circuit for Y = A’ B’ C’ + A’ B C + A B’ C’ • Suppose we have an unknown digital circuit, represented by the given block box and conditions for high output. All we know is which terminals are inputs, which are output, and how to connect power. Given only that information, we can find the Boolean expression of the output....
View Full Document

Page1 / 42

Lec5_BooleanAlgebra_11_updated - 1 Lecture 5 Boolean...

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