Redstone Circuits and Computer Logic in Minecraft

Introduction to Redstone

• Redstone can act like a cable to produce outputs
• Output: 0 (off) or 1 (on)

Basic Circuits

• Simple Circuit: Lamp controlled by pistons
  • Both pistons off -> Lamp off (0)
  • One piston on -> Lamp off (0)
  • Both pistons on -> Lamp on (1)
• AND Gate: Outputs 1 when both inputs are 1
  • Truth Table: Output is true if both blue and green inputs are true

Pistons as Transistors

• Transistors control the flow of electricity
• Voltage applied -> Current flows through (like piston in AND gate)

Logic Gates

• NOT Gate: Inverts the signal
• NAND Gate: Combines NOT and AND gates
  • Significance: Any logic function can be implemented using only NAND gates

Compact Redstone Circuits

• Redstone circuits can be made more compact
• Useful for more complex components

Binary Arithmetic

• Half Adder: Adds two binary digits using 5 NAND gates
  • Only adds up to 2
• Full Adder: Adds three binary digits using 9 NAND gates
  • Has an additional carry-in input for previous operations
  • Allows chaining to create multi-bit adders (e.g., 4-bit adder)

Conversion and Display

• Binary to Decimal:
  • Computers use binary (0, 1) vs. humans use decimal (0-9)
  • Example: 23 in decimal = 10111 in binary
• Seven-Segment Display:
  • Converts binary to more readable decimal digits
  • Used in real-world applications (e.g., digital clocks, calculators)

Arithmetic Logic Unit (ALU)

• Combines addition and subtraction
  • Example: 2 + 3 = 5 (Addition)
  • Example: 2 - 3 = -1 (Subtraction)
• ALU processes basic arithmetic operations

Building a Computer in Minecraft

• Memory and Storage:
  • Use latches to store single bits
  • Repeaters can store state for registers
  • Registers store numbers for ALU processing
  • Programs stored as binary-encoded instructions
• Assembler: Converts assembly code into machine code for easier programming
• Memory Architectures:
  • Harvard: Separate instruction and data memory
  • von Neumann: Combined instruction and data memory

Central Processing Unit (CPU)

• CPU fetches, decodes, and executes instructions
• Complex to build from scratch, useful to follow designs like "mattbatwings" CPU design
• Example Program: Fibonacci counter

Advanced Topics (Mentioned Lightly)

• Pipelining
• Cache hierarchy
• Vector parallelism
• Branch prediction
• ISA extensions
• Clock gating

Conclusion

• Redstone logic enables building a full-fledged computer in Minecraft