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binary-encoding

Gray Code Explained: Why Rotary Encoders Use It

TL;DR: Gray code is a binary numeral system where successive values differ by exactly one bit. Rotary encoders, FIFO pointers, and Karnaugh maps use it because single-bit transitions eliminate the...

7 min read
error-correction

Hamming Code Error Correction Explained (with Math)

TL;DR: A Hamming(7,4) code adds three parity bits to four data bits so that any single-bit flip — whether in a data bit or in a parity bit itself —...

8 min read
cpu-architecture

How a Microprocessor Works: Fetch-Decode-Execute Deep Dive

TL;DR: A microprocessor repeats one loop forever: fetch the next instruction from memory using the program counter, decode it into control signals, then execute it on the ALU and registers....

20 min read
alu

How an ALU Works: Arithmetic Logic Unit from Gates

TL;DR: An Arithmetic Logic Unit (ALU) is a combinational circuit inside a CPU that performs arithmetic operations (addition, subtraction) and bitwise logic operations (AND, OR, XOR, NOT, shifts) on two...

7 min read
number-systems

IEEE 754 Floating Point: From Bits to Numbers

TL;DR: IEEE 754 represents real numbers as , with a sign bit, a biased exponent, and a mantissa whose leading 1 is implicit. The format reserves specific exponent values for...

9 min read
cpu-architecture

Instruction Register and the Decode Stage

TL;DR: The instruction register (IR) holds the binary instruction word fetched from memory. The decode stage splits that word into fields — opcode, register addresses, immediate — and feeds each...

8 min read
state-machines

Mealy vs Moore State Machines: With Examples

TL;DR: A Mealy machine's outputs depend on both the current state and the current inputs; a Moore machine's outputs depend only on the current state. Mealy machines tend to use...

14 min read
error-detection

Parity Bit Tutorial: Single-Bit Error Detection

TL;DR: A parity bit is one extra bit appended to a binary word so that the total number of 1s is even (even parity) or odd (odd parity). A chain...

7 min read
priority-encoder

Priority Encoder Explained: 4-to-2 and 8-to-3

TL;DR: A priority encoder is a combinational circuit that takes N input lines and outputs a -bit binary code identifying the highest-priority active input. Unlike a plain encoder (which assumes...

7 min read
cpu-architecture

Program Counter Explained: The CPU's Bookmark

TL;DR: The program counter (PC) is the register that holds the memory address of the next instruction a CPU will fetch. It increments automatically after every fetch, but branch and...

9 min read
memory

RAM vs ROM: The Essential Difference (with Circuits)

TL;DR: RAM is volatile read-write memory used as the CPU's working scratchpad; ROM is non-volatile read-mostly memory used to hold firmware and constants. Both are arrays of single-bit cells selected...

9 min read
simcast

SimCast Lessons: Step-Through Circuit Tutorials

TL;DR: SimCast lessons are step-by-step animated circuit tutorials inside DigiSim. Each step adds components, draws wires, and updates values while a narrator explains in your chosen language. You pause anywhere,...

9 min read
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