2024-03-18

Introduction

Summary

keywords

TODO

HW

Exercise*

Next time

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Gray code

The codes are sequenced so as the adjacent code has only one bit difference.

Why do we need concept of gray codes?

• To detect how many bits are corrupted in the data.

• When the data is changed, the value difference is equal to the number of corrupted bits.

Error Detection Codes

1. Parity bits

• It adjusts so that the number f 1s in a group to be even(even parity) or odd(odd parity)

• It cannot correctly detect multiple bit errors.

• It cannot fix errors.

Serial Data Bit representation

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Boolean Algebra

Diagrams, truth table, and function.

• The dot symbol stands for 'not' operation; the triangle symbol stands for 'buffer' operation. Combined, it means 'not' operation.

• truth table is the only definitive way to express operation.

• truth table uses "HIGH", "LOW", "X" as the entity(Due to the underlying hardware tech).

• X means either Low or high logic level: Don't care condition

• not is typographically expressed in prime or overbar.

• overbar is a complement expression.

useful two-binary-variable operations

• AND $F(x_1,x_2) = x_1 x_2$

• OR $F(x_1,x_2) = x_1+x_2$

• XOR (OR, but not both) $F(x_1,x_2) = x_1⊕x_2$

• NAND

• NOR

• E-XOR

• NAND, NOR has duality

• All the other operations can be implemented with NAND and NOR gates; it is universal.

Logic Circuits

There are canonical form or others. Canonical form definitively expresses truth tables.

Basic Axioms of Boolean Algebra

• only concerns three operations only (AND, OR, Complement)