Boolean algebra and digital logic, explained — with live examples you can build yourself.
An introduction to Boolean algebra: variables, the three core operations, and the laws that let you simplify any logical expression.
What a truth table is, how to build one by hand, and how it connects directly to logic gates and circuit verification.
How De Morgan's laws let you convert any AND/OR expression into an equivalent built entirely from NAND or NOR gates.
A visual technique for minimizing Boolean expressions by grouping adjacent 1s in a grid — fewer gates, faster and cheaper circuits.
The key difference between level-sensitive latches and edge-triggered flip-flops, and why it matters for reliable digital memory.
How binary addition is built from XOR and AND gates, and how chaining full adders produces a complete N-bit adder.
How select lines let a multiplexer route one of several inputs to a single output, and why demultiplexers do the exact opposite.
How positional number systems work, and how to convert between binary, decimal, and hexadecimal — the foundation for reading any digital schematic.
How a chain of flip-flops counts in binary, the difference between ripple and synchronous counters, and where counters show up in real circuits.
How chained flip-flops shift bits left or right each clock cycle, and why shift registers are the standard tool for serial-to-parallel conversion.
How a decoder activates exactly one output line from a binary address, and how an encoder does the reverse — the backbone of memory addressing.
How an Arithmetic-Logic Unit combines adders, logic gates, and a multiplexer to perform multiple operations selected by an opcode.
How RAM stores data in an array of latches addressed by a decoder, why ROM is wired permanently, and where each type is used in a real system.
Why Gray code changes only one bit between consecutive values, and how a parity bit gives circuits a cheap way to detect single-bit errors.
How a comparator circuit determines whether one binary number is greater than, equal to, or less than another, one bit — or one nibble — at a time.
Why every flip-flop in a circuit should share one clock, and what happens — metastability — when an input changes too close to the clock edge.
How an FPGA implements arbitrary logic using configurable look-up tables instead of fixed gates, and how Boolflow's PLM blocks model the same idea.