No. 2-1

Chapter #2: Two-Level Combinational Logic

No. 2-2

Motivatio

n

Rapid prototyping technology

Use of computer aided design tools: espresso

Design Techniques that Spanning Multiple Technologies

Transistor-Transistor Logic (TTL)

Complementary Metal on Oxide Silicon (CMOS)

Multiple Design Representations

Truth Tables

Static gate descriptions

Dynamic waveform descriptions

Further Amplification on the Concepts of Chapter #1:

No. 2-3

Chapter Overview

Logic Functions and Switches

Not, AND, OR, NAND, NOR, XOR, XNOR

Gate Logic

Laws and Theorems of Boolean Algebra

Two Level Canonical Forms

Incompletely Specified Functions

Two Level Simplification

Boolean Cubes

Karnaugh Maps

Quine-McClusky Method

Espresso Method

No. 2-4

Logic Functions: Boolean Algebra

is Algebraic structure consisting of:

set of elements B

binary operations {+, •}

unary operation {'}

such that the following axioms hold:

1. B contains at least two elements, a, b, such that a ≠ b

2. Closure a,b in B,

(i) a + b in B

(ii) a • b in B

3. Commutative Laws: a,b in B,

(i) a + b = b + a

(ii) a • b = b • a

4. Identities: 0, 1 in B

(i) a + 0 = a

(ii) a • 1 = a

5. Distributive Laws:

(i) a + (b • c) = (a + b) •(a + c)

(ii) a •(b + c) = a b + a • c

6. Complement:

(i) a + a' = 1

(ii) a • a' = 0

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