2024-03-18
Introduction
Summary
keywords
TODO
HW
Exercise*
Next time
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
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)
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