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General #

• bit just comes from “binary digit”
• UPC’s are just encoded in bits with the bars
• Parity: even parity if even number of 1’s and odd parity if od number

0x #

• Why hexadecimal? In hexidecimal, a multi-byte number is represented as the combination of the bights that comprise it
  • Each byte can be divided into an equal number of bits (2 sets of 4 bits)

Boolean algebra #

• OR and AND correspond to union and intersection
• + (or ^) corresponds to union, and x (or downcaret) to intersection
• NOT corresponds to 1 - something

Representing this in a circuit #

This is actually quite intuitive. Pg. 100-101 of Code: The Hidden Language of Computer Hardware and Software is probably the best visualization I have seen of this

• switches in series - AND
• switches in parallel - OR
• You can combine these to produce complex logic gates. For example, each OR of the condition is a separate path of the circuitry where if fulfilled, current will flow through. AND’s as well. These electrical switches - relays - are the building blocks of circuits. Connecting them allows you to build these gates.
• Thus, if you can simplify the expression designing the logic gate, you can simplify the circuit needed to model it.

Logic Gates #

Core building blocks #

These are all intuitive - take some time to think about it

• AND: 2 relays in series - AND gate
• OR: 2 relays in parallel - OR gate
• NOT: A relay where the circuit is connected when the switch is in the off state - called an inverter - used for NOT’s. Input != output
  • Inverts voltage to no voltage and vice versa
• NOR: 2 relays wired in series with circuit connected in off position
• NAND: 2 relays wire in parallel with circuit connected in off position
• BUFFER: single relay that connects the circuit when it is on. Input = output
  • can delay or amplify signals

Other Gates #

• XOR: Combination of OR and NAND