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Introduction

Summary

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TODO

HW

Exercise*

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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​

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)