Tutorials, deep dives into digital logic concepts, circuit design guides, and DigiSim platform updates.https://digisim.io/en-ushttps://digisim.io/blog/bcd-binary-coded-decimal-fundamentals/https://digisim.io/blog/bcd-binary-coded-decimal-fundamentals/BCD encodes each decimal digit as 4 bits, avoiding the rounding errors of binary fractions. Packed vs unpacked, the +6 add-correction, and where BCD lives.Thu, 07 May 2026 00:00:00 GMTbcdnumber-systemsarithmeticdecimal-encodingdennyhttps://digisim.io/blog/bcd-to-7-segment-decoder-from-numbers-to-display/https://digisim.io/blog/bcd-to-7-segment-decoder-from-numbers-to-display/Map a 4-bit BCD digit to the seven segments of a digital display using a truth table, K-map minimization, and the classic 74LS47 driver chip.Thu, 07 May 2026 00:00:00 GMTdecodersseven-segment-displaybcdkarnaugh-mapsdennyhttps://digisim.io/blog/best-digital-logic-simulators-2026/https://digisim.io/blog/best-digital-logic-simulators-2026/An honest, side-by-side ranking of the top digital logic simulators in 2026 — DigiSim, Logisim Evolution, CircuitVerse, Tinkercad, Falstad, and Digital.Thu, 07 May 2026 00:00:00 GMTcomparisondigital-logicsimulatorstoolsdennyhttps://digisim.io/blog/booth-multiplier-explained-with-examples/https://digisim.io/blog/booth-multiplier-explained-with-examples/Booth's algorithm multiplies signed binary numbers by examining bit pairs and choosing add, subtract, or skip. Walk -3 x 5 step-by-step and see the hardware.Thu, 07 May 2026 00:00:00 GMTbooth-multipliersigned-multiplicationtwos-complementcpu-arithmeticdennyhttps://digisim.io/blog/build-a-cpu-from-scratch-in-a-simulator/https://digisim.io/blog/build-a-cpu-from-scratch-in-a-simulator/A complete walkthrough for building a working 8-bit CPU from logic gates: registers, ALU, bus, RAM, control unit, and a runnable three-instruction program.Thu, 07 May 2026 00:00:00 GMTcpu-architecturedigital-logicinteractive-tutorialhowtodennyhttps://digisim.io/blog/carry-lookahead-adder-faster-than-ripple-carry/https://digisim.io/blog/carry-lookahead-adder-faster-than-ripple-carry/A carry-lookahead adder computes all carries in parallel from generate and propagate signals. Walk the equations, see the gate count, compare to ripple-carry.Thu, 07 May 2026 00:00:00 GMTcarry-lookahead-adderclagenerate-propagatehigh-speed-arithmeticdennyhttps://digisim.io/blog/clock-skew-and-its-effect-on-timing/https://digisim.io/blog/clock-skew-and-its-effect-on-timing/Clock skew is the edge arrival-time difference between flip-flops. How positive and negative skew change setup and hold, plus clock-tree synthesis basics.Thu, 07 May 2026 00:00:00 GMTclock-skewtimingsequential-logicclock-distributiondennyhttps://digisim.io/blog/cpu-flags-register-carry-zero-overflow-sign/https://digisim.io/blog/cpu-flags-register-carry-zero-overflow-sign/How the four standard CPU flags Z, C, N, and V are generated from ALU results and how conditional branches read them to control program flow.Thu, 07 May 2026 00:00:00 GMTcpu-architectureflags-registeraluconditional-branchdennyhttps://digisim.io/blog/demultiplexer-tutorial-1-to-4-and-1-to-8/https://digisim.io/blog/demultiplexer-tutorial-1-to-4-and-1-to-8/A demultiplexer routes one input to one of several outputs based on a select code. Learn the truth tables, gate-level designs, and where DEMUX shows up in CPUs.Thu, 07 May 2026 00:00:00 GMTdemultiplexercombinational-logicdecodercpu-architecturedennyhttps://digisim.io/blog/digisim-vs-circuitverse/https://digisim.io/blog/digisim-vs-circuitverse/Two strong browser-based digital logic simulators compared honestly — DigiSim's curriculum and animations vs CircuitVerse's open-source community and free pricing.Thu, 07 May 2026 00:00:00 GMTcomparisoncircuitversedigisimdigital-logicdennyhttps://digisim.io/blog/digisim-vs-logisim-evolution/https://digisim.io/blog/digisim-vs-logisim-evolution/A fair head-to-head between DigiSim.io and Logisim Evolution — what each does best, where each falls short, and how to pick the right one for your course.Thu, 07 May 2026 00:00:00 GMTcomparisonlogisim-evolutiondigisimdigital-logicdennyhttps://digisim.io/blog/digisim-vs-tinkercad-circuits/https://digisim.io/blog/digisim-vs-tinkercad-circuits/DigiSim and Tinkercad Circuits target different audiences — DigiSim for pure digital logic and CPU architecture, Tinkercad for Arduino, breadboarding, and analog work.Thu, 07 May 2026 00:00:00 GMTcomparisontinkercaddigisimelectronics-educationdennyhttps://digisim.io/blog/digital-comparator-explained-equality-and-magnitude/https://digisim.io/blog/digital-comparator-explained-equality-and-magnitude/A digital comparator tests whether two binary numbers are equal, or which one is larger. See the XNOR-AND equality circuit, magnitude logic, and 8-bit cascading.Thu, 07 May 2026 00:00:00 GMTcomparatorcombinational-logicxnoraludennyhttps://digisim.io/blog/digital-logic-roadmap-from-gates-to-cpu-in-30-days/https://digisim.io/blog/digital-logic-roadmap-from-gates-to-cpu-in-30-days/A day-by-day digital logic curriculum: 30 days of focused lessons, one blog post and one interactive template per day, from AND gates to a working CPU.Thu, 07 May 2026 00:00:00 GMTlearning-roadmapdigital-logic-curriculumcpu-designself-studydennyhttps://digisim.io/blog/dont-care-conditions-in-karnaugh-maps/https://digisim.io/blog/dont-care-conditions-in-karnaugh-maps/Don't-cares mark inputs that never occur or whose output is irrelevant. Treat them as 0 or 1, whichever shrinks the K-map cover, and BCD logic collapses fast.Thu, 07 May 2026 00:00:00 GMTkarnaugh-mapsdont-caresboolean-algebralogic-minimizationdennyhttps://digisim.io/blog/embed-an-interactive-circuit-in-your-lesson-or-blog/https://digisim.io/blog/embed-an-interactive-circuit-in-your-lesson-or-blog/Embed any DigiSim template as a live, interactive iframe. Step-by-step for Canvas, Moodle, WordPress, Notion, and Ghost — with copy-paste HTML.Thu, 07 May 2026 00:00:00 GMTembediframelmseducator-toolsdennyhttps://digisim.io/blog/endianness-big-vs-little-with-bus-diagrams/https://digisim.io/blog/endianness-big-vs-little-with-bus-diagrams/Big-endian puts the most-significant byte at the lowest address; little-endian flips it. Bus diagrams, 0x12345678 layouts, and why x86 and TCP/IP differ.Thu, 07 May 2026 00:00:00 GMTendiannessmemory-layoutcpu-architecturedata-representationdennyhttps://digisim.io/blog/free-online-circuit-simulators-compared/https://digisim.io/blog/free-online-circuit-simulators-compared/An honest 2026 comparison of free online circuit simulators — DigiSim, CircuitVerse, Tinkercad, Falstad — what's free, what's paywalled, and which fits which use case.Thu, 07 May 2026 00:00:00 GMTcomparisonfree-toolsonline-simulatorsdigital-logicdennyhttps://digisim.io/blog/gray-code-explained-and-why-rotary-encoders-use-it/https://digisim.io/blog/gray-code-explained-and-why-rotary-encoders-use-it/Gray code numbers adjacent values that differ by exactly one bit. Learn the binary-to-Gray formula, why rotary encoders rely on it, and the hardware impact.Thu, 07 May 2026 00:00:00 GMTgray-coderotary-encodersbinary-encodingclock-domain-crossingdennyhttps://digisim.io/blog/hamming-code-error-correction-explained/https://digisim.io/blog/hamming-code-error-correction-explained/Hamming(7,4) corrects single-bit errors with three parity bits. Walk the syndrome math, encode 1011, flip a bit, and recover the original word step-by-step.Thu, 07 May 2026 00:00:00 GMThamming-codeerror-correctionparitycoding-theorydennyhttps://digisim.io/blog/how-a-microprocessor-works-fetch-decode-execute-deep-dive/https://digisim.io/blog/how-a-microprocessor-works-fetch-decode-execute-deep-dive/A textbook-grade tour of the microprocessor: von Neumann architecture, buses, microoperations, decoding, ALU execution, branching, memory hierarchy, and pipelining.Thu, 07 May 2026 00:00:00 GMTcpu-architecturefetch-decode-executevon-neumannmicrooperationsdennyhttps://digisim.io/blog/how-an-alu-works-arithmetic-logic-unit-from-gates/https://digisim.io/blog/how-an-alu-works-arithmetic-logic-unit-from-gates/An Arithmetic Logic Unit performs every math and bitwise operation a CPU executes. See how a 4-bit ALU is built from adders, comparators, and a multiplexer.Thu, 07 May 2026 00:00:00 GMTalucpu-architecturearithmeticcombinational-logicdennyhttps://digisim.io/blog/ieee-754-floating-point-from-bits-to-numbers/https://digisim.io/blog/ieee-754-floating-point-from-bits-to-numbers/Decode 32 and 64-bit IEEE 754 layouts: sign, biased exponent, mantissa, and the implicit leading 1. Walk encode/decode examples and see why floats aren't associative.Thu, 07 May 2026 00:00:00 GMTieee-754floating-pointfpunumerical-representationdennyhttps://digisim.io/blog/instruction-register-and-the-decode-stage/https://digisim.io/blog/instruction-register-and-the-decode-stage/How the instruction register holds a fetched binary word and how the decoder cracks it into opcode, register addresses, and immediate fields.Thu, 07 May 2026 00:00:00 GMTcpu-architectureinstruction-registercontrol-unitinstruction-decodedennyhttps://digisim.io/blog/mealy-vs-moore-state-machines-with-examples/https://digisim.io/blog/mealy-vs-moore-state-machines-with-examples/The difference between Mealy and Moore finite state machines, worked traffic-light and sequence-detector examples, encoding choices, and how to pick one.Thu, 07 May 2026 00:00:00 GMTstate-machinessequential-logicfsm-designdigital-logicdennyhttps://digisim.io/blog/parity-bit-tutorial-single-bit-error-detection/https://digisim.io/blog/parity-bit-tutorial-single-bit-error-detection/A parity bit is one extra bit appended to a word so the total bit count is even or odd. Build the XOR generator and checker, see the limits, and apply it.Thu, 07 May 2026 00:00:00 GMTparity-biterror-detectionxor-gateserial-protocolsdennyhttps://digisim.io/blog/priority-encoder-explained-4-to-2-and-8-to-3/https://digisim.io/blog/priority-encoder-explained-4-to-2-and-8-to-3/A priority encoder converts an N-bit one-hot or many-hot input into a binary index, breaking ties by priority. See the truth tables and gate-level designs.Thu, 07 May 2026 00:00:00 GMTencoderpriority-encodercombinational-logicinterrupt-controllerdennyhttps://digisim.io/blog/program-counter-explained-the-cpus-bookmark/https://digisim.io/blog/program-counter-explained-the-cpus-bookmark/How the program counter tracks the next instruction, increments automatically, and gets overwritten by branches and jumps inside every CPU.Thu, 07 May 2026 00:00:00 GMTcpu-architectureprogram-counterregisterscontrol-flowdennyhttps://digisim.io/blog/ram-vs-rom-the-essential-difference-with-circuits/https://digisim.io/blog/ram-vs-rom-the-essential-difference-with-circuits/Compare RAM and ROM by volatility, write capability, density, and cost; then trace how an address decoder selects a word line and reads the bit lines.Thu, 07 May 2026 00:00:00 GMTmemoryramromcpu-architecturedennyhttps://digisim.io/blog/simcast-lessons-step-through-circuit-tutorials/https://digisim.io/blog/simcast-lessons-step-through-circuit-tutorials/SimCast turns DigiSim into an interactive textbook: animated, narrated lessons that build circuits step by step in 7 languages. Pause, replay, follow along.Thu, 07 May 2026 00:00:00 GMTsimcastlessonsinteractive-tutorialeducator-toolsdennyhttps://digisim.io/blog/siso-sipo-piso-pipo-shift-register-modes/https://digisim.io/blog/siso-sipo-piso-pipo-shift-register-modes/Shift-register modes SISO, SIPO, PISO, PIPO cover delay lines, UART RX/TX, and parallel registers. Diagrams, worked timing, and the 74194 universal part.Thu, 07 May 2026 00:00:00 GMTshift-registerssequential-logicuartserial-communicationdennyhttps://digisim.io/blog/static-vs-dynamic-hazards-in-combinational-logic/https://digisim.io/blog/static-vs-dynamic-hazards-in-combinational-logic/Combinational circuits glitch when paths race. Learn how static-1, static-0, and dynamic hazards arise, and how a redundant K-map cover term eliminates them.Thu, 07 May 2026 00:00:00 GMThazardscombinational-logictimingkarnaugh-mapsdennyhttps://digisim.io/blog/tri-state-buffers-and-bus-arbitration-explained/https://digisim.io/blog/tri-state-buffers-and-bus-arbitration-explained/Tri-state buffers add a high-impedance third state so multiple drivers can share one bus without contention. Learn the cell, the enable logic, and arbitration.Thu, 07 May 2026 00:00:00 GMTtri-state-bufferbus-architecturearbitrationcpu-architecturedennyhttps://digisim.io/blog/twos-complement-explained-signed-binary-arithmetic/https://digisim.io/blog/twos-complement-explained-signed-binary-arithmetic/Why every modern CPU uses two's complement for signed numbers: encoding, negation, sign extension, overflow detection, and why addition just works.Thu, 07 May 2026 00:00:00 GMTbinary-arithmetictwos-complementcpu-architecturedigital-logicdennyhttps://digisim.io/blog/using-the-oscilloscope-to-debug-digital-circuits/https://digisim.io/blog/using-the-oscilloscope-to-debug-digital-circuits/Place an oscilloscope, connect channels to clock and data, and read waveforms to spot clock-to-Q delay, glitches, and setup violations in DigiSim.Thu, 07 May 2026 00:00:00 GMToscilloscopedebuggingtiming-analysisdigisim-workflowdennyhttps://digisim.io/blog/digital-logic-101-your-first-steps-with-and-or-and-not-gates/https://digisim.io/blog/digital-logic-101-your-first-steps-with-and-or-and-not-gates/AND, OR, and NOT are the three fundamental logic gates. This beginner's guide builds each from scratch and combines them into a NAND in your browser.Wed, 14 Jan 2026 00:00:00 GMTand-gateor-gatenot-gatedigital-logic-101dennyhttps://digisim.io/blog/mastering-boolean-algebra-the-foundation-of-digital-circuit/https://digisim.io/blog/mastering-boolean-algebra-the-foundation-of-digital-circuit/Boolean algebra defines how circuits manipulate TRUE and FALSE. Covers AND/OR/NOT primitives plus identity, absorption, and De Morgan's theorems.Wed, 14 Jan 2026 00:00:00 GMTboolean-algebralogic-lawscircuit-optimizationde-morgans-lawsdennyhttps://digisim.io/blog/mastering-de-morgans-laws-the-key-to-efficient-digital/https://digisim.io/blog/mastering-de-morgans-laws-the-key-to-efficient-digital/De Morgan's Laws convert NAND to bubbled-OR and NOR to bubbled-AND. Apply them to build NAND-only or NOR-only circuits and optimize multi-level logic.Wed, 14 Jan 2026 00:00:00 GMTde-morgans-lawsnand-gatecircuit-optimizationuniversal-gatesdennyhttps://digisim.io/blog/propagation-delay-the-physics-that-dictates-digital-speed/https://digisim.io/blog/propagation-delay-the-physics-that-dictates-digital-speed/Propagation delay is the time a logic gate takes to react to an input change. It sets the critical path, max clock frequency, and circuit glitch behavior.Wed, 14 Jan 2026 00:00:00 GMTpropagation-delaytiming-analysiscritical-pathcircuit-speeddennyhttps://digisim.io/blog/the-unsung-hero-how-the-nor-gate-built-apollo-and-powers/https://digisim.io/blog/the-unsung-hero-how-the-nor-gate-built-apollo-and-powers/The Apollo Guidance Computer was built almost entirely from NOR gates. Functional completeness, reliability via uniformity, and CMOS-implementation limits.Wed, 14 Jan 2026 00:00:00 GMTnor-gateuniversal-gatesapollo-computercomputing-historydennyhttps://digisim.io/blog/beyond-sum-of-products-mastering-product-of-sums-for/https://digisim.io/blog/beyond-sum-of-products-mastering-product-of-sums-for/Product of Sums (POS) is the dual of SOP, built from the 0s of a truth table. Derive maxterms, build OR-AND circuits, and contrast POS with SOP.Tue, 13 Jan 2026 00:00:00 GMTproduct-of-sumsboolean-algebracircuit-optimizationcombinational-logicdennyhttps://digisim.io/blog/beyond-two-inputs-mastering-multi-input-logic-gates-for-high/https://digisim.io/blog/beyond-two-inputs-mastering-multi-input-logic-gates-for-high/Multi-input logic gates compress wide buses into single signals. Compare cascade vs tree implementations and pick the right one for your design.Tue, 13 Jan 2026 00:00:00 GMTmulti-input-gatespropagation-delayfan-inlogic-gatesdennyhttps://digisim.io/blog/case-study-visualizing-the-fetch-decode-execute-cycle/https://digisim.io/blog/case-study-visualizing-the-fetch-decode-execute-cycle/Step through every microoperation of a CPU's fetch-decode-execute cycle: program counter, instruction register, ALU, and control unit at the bit level.Tue, 13 Jan 2026 00:00:00 GMTcpu-architecturefetch-decode-executecase-studyinteractive-simulationdennyhttps://digisim.io/blog/counters-and-state-machines-controlling-digital-sequences/https://digisim.io/blog/counters-and-state-machines-controlling-digital-sequences/Counters cycle through binary sequences each clock pulse; FSMs extend that with conditional transitions. Build both and derive a traffic-light FSM.Tue, 13 Jan 2026 00:00:00 GMTcountersstate-machinessequential-logicfinite-state-machinedennyhttps://digisim.io/blog/decoders-and-encoders-driving-a-7-segment-display/https://digisim.io/blog/decoders-and-encoders-driving-a-7-segment-display/Decoders translate binary into one-hot or segment outputs; encoders do the reverse. Build a BCD-to-7-segment driver and learn priority encoders.Tue, 13 Jan 2026 00:00:00 GMTdecodersencoders7-segment-displaycombinational-logicdennyhttps://digisim.io/blog/decoding-digital-logic-mastering-ansi-vs-iec-symbols-on/https://digisim.io/blog/decoding-digital-logic-mastering-ansi-vs-iec-symbols-on/ANSI uses distinctive shapes per gate; IEC uses uniform rectangles with '&' or '≥1' qualifiers. Both encode the same Boolean logic — read either fluently.Tue, 13 Jan 2026 00:00:00 GMTansi-symbolsiec-symbolsschematic-readinglogic-notationdennyhttps://digisim.io/blog/grading-circuits-in-seconds-the-digisim-workflow/https://digisim.io/blog/grading-circuits-in-seconds-the-digisim-workflow/Cut circuit-lab grading time by 80% with DigiSim.io shareable URLs. Test student submissions functionally, apply rubrics, and give feedback fast.Tue, 13 Jan 2026 00:00:00 GMTeducationdigisim-workflowdennyhttps://digisim.io/blog/mastering-frequency-division-from-flip-flops-to-modulo-n/https://digisim.io/blog/mastering-frequency-division-from-flip-flops-to-modulo-n/Frequency division produces a slow clock from a fast one using flip-flops or counters. Build a divider chain, UART baud generator, and PWM timer.Tue, 13 Jan 2026 00:00:00 GMTfrequency-divisiont-flip-flopmodulo-n-counterclock-signaldennyhttps://digisim.io/blog/mastering-sequential-logic-the-d-latch-explained-and/https://digisim.io/blog/mastering-sequential-logic-the-d-latch-explained-and/The D latch fixes the SR latch's forbidden state by tying Set and Reset to one Data input gated by Enable. Derive the characteristic equation here.Tue, 13 Jan 2026 00:00:00 GMTd-latchsequential-logicsr-latchtransparent-latchdennyhttps://digisim.io/blog/multiplexers-mux-demystified-the-data-traffic-controller/https://digisim.io/blog/multiplexers-mux-demystified-the-data-traffic-controller/A multiplexer routes one of $2^n$ inputs to a single output via n select lines. Build 2-to-1 and 4-to-1 MUXes and use them as universal function generators.Tue, 13 Jan 2026 00:00:00 GMTmultiplexercombinational-logicdata-routingcpu-architecturedennyhttps://digisim.io/blog/sr-vs-jk-flip-flops-the-basics-of-sequential-logic/https://digisim.io/blog/sr-vs-jk-flip-flops-the-basics-of-sequential-logic/The JK flip-flop solves the SR latch's forbidden state by redefining J=K=1 as toggle. Compare both, derive excitation tables, and build counters from each.Tue, 13 Jan 2026 00:00:00 GMTflip-flopssequential-logicsr-latchjk-flip-flopdennyhttps://digisim.io/blog/the-and-gate-foundation-of-digital-logic-and-decision-making/https://digisim.io/blog/the-and-gate-foundation-of-digital-logic-and-decision-making/The AND gate outputs 1 only when every input is 1. Explore its truth table, Boolean algebra, propagation delay, and use in bit masking and clock gating.Tue, 13 Jan 2026 00:00:00 GMTand-gatelogic-gatestruth-tablespropagation-delaydennyhttps://digisim.io/blog/the-clock-pulse-why-computers-need-a-heartbeat/https://digisim.io/blog/the-clock-pulse-why-computers-need-a-heartbeat/The clock signal is the periodic square wave that synchronizes every flip-flop in a synchronous system. Covers frequency, duty cycle, skew, and jitter.Tue, 13 Jan 2026 00:00:00 GMTclock-signaltimingsynchronous-designdigital-logic-101dennyhttps://digisim.io/blog/the-d-flip-flop-the-unsung-hero-of-synchronous-digital/https://digisim.io/blog/the-d-flip-flop-the-unsung-hero-of-synchronous-digital/The D flip-flop captures its D input on a single clock edge — the snapshot behavior every synchronous register needs. Covers timing and metastability.Tue, 13 Jan 2026 00:00:00 GMTd-flip-flopsequential-logicedge-triggeringmetastabilitydennyhttps://digisim.io/blog/the-end-of-the-breadboard-why-virtual-labs-are-here-to-stay/https://digisim.io/blog/the-end-of-the-breadboard-why-virtual-labs-are-here-to-stay/Browser-based simulators offer faster feedback, better signal visibility, and lower cost than physical breadboards. A hybrid model uses each where it excels.Tue, 13 Jan 2026 00:00:00 GMTeducationvirtual-labsbreadboarddigisim-workflowdennyhttps://digisim.io/blog/the-half-adder-vs-the-full-adder-how-computers-do-math/https://digisim.io/blog/the-half-adder-vs-the-full-adder-how-computers-do-math/Half adders sum two bits and produce a carry; full adders sum three bits (including carry-in). Chain full adders to build multi-bit ripple-carry adders.Tue, 13 Jan 2026 00:00:00 GMThalf-adderfull-adderbinary-additionarithmetic-circuitsdennyhttps://digisim.io/blog/the-half-adder-your-first-step-into-digital-logic-design/https://digisim.io/blog/the-half-adder-your-first-step-into-digital-logic-design/A half adder uses an XOR gate for the Sum and an AND gate for the Carry to add two single bits — the foundational atom of all binary arithmetic.Tue, 13 Jan 2026 00:00:00 GMThalf-adderbinary-additionxor-gatearithmetic-circuitsdennyhttps://digisim.io/blog/the-humble-not-gate-inversions-power-in-digital-logic/https://digisim.io/blog/the-humble-not-gate-inversions-power-in-digital-logic/The NOT gate inverts its single input: 0 becomes 1, 1 becomes 0. From ring oscillators to active-low signaling, inversion is the operation logic needs.Tue, 13 Jan 2026 00:00:00 GMTnot-gateinverterlogic-gatespropagation-delaydennyhttps://digisim.io/blog/the-jk-flip-flop-mastering-the-universal-building-block-of/https://digisim.io/blog/the-jk-flip-flop-mastering-the-universal-building-block-of/The JK flip-flop has four modes — hold, set, reset, toggle — selected by J and K at each clock edge. It's the universal cell of counters and state machines.Tue, 13 Jan 2026 00:00:00 GMTjk-flip-flopsequential-logictoggle-modecountersdennyhttps://digisim.io/blog/the-johnson-counter-mastering-the-twisted-ring-for-efficient/https://digisim.io/blog/the-johnson-counter-mastering-the-twisted-ring-for-efficient/A Johnson counter is a shift register with the inverted last output fed back to the first stage, giving 2n states from n flip-flops and 2-input decoding.Tue, 13 Jan 2026 00:00:00 GMTjohnson-counterring-countersequential-logiccountersdennyhttps://digisim.io/blog/the-nand-gate-the-single-building-block-of-all-digital-logic/https://digisim.io/blog/the-nand-gate-the-single-building-block-of-all-digital-logic/The NAND gate is functionally complete: AND, OR, NOT, XOR, and memory cells all build from NAND alone. CMOS economics make it the dominant standard cell.Tue, 13 Jan 2026 00:00:00 GMTnand-gateuniversal-gatesfunctional-completenesscircuit-designdennyhttps://digisim.io/blog/the-or-gate-understanding-digital-logics-democratic/https://digisim.io/blog/the-or-gate-understanding-digital-logics-democratic/The OR gate outputs 1 if any input is 1. Truth table, Boolean expression, propagation timing, and uses in CPU interrupts, safety systems, and bus arbitration.Tue, 13 Jan 2026 00:00:00 GMTor-gatelogic-gatestruth-tablescpu-interruptsdennyhttps://digisim.io/blog/the-t-flip-flop-the-unsung-hero-of-digital-counting-and/https://digisim.io/blog/the-t-flip-flop-the-unsung-hero-of-digital-counting-and/The T flip-flop toggles on each clock edge when T=1, making it the canonical building block of frequency dividers, ripple counters, and modulo-N timers.Tue, 13 Jan 2026 00:00:00 GMTt-flip-flopcountersfrequency-divisionsequential-logicdennyhttps://digisim.io/blog/the-unseen-clock-mastering-setup-hold-and-metastability-in/https://digisim.io/blog/the-unseen-clock-mastering-setup-hold-and-metastability-in/Setup and hold times define a forbidden window around each clock edge. Violations cause metastability — mitigated by 2-flip-flop synchronizers.Tue, 13 Jan 2026 00:00:00 GMTsetup-hold-timemetastabilitytiming-analysissynchronous-designdennyhttps://digisim.io/blog/the-unsung-hero-why-digital-buffers-are-essential-in-circuit/https://digisim.io/blog/the-unsung-hero-why-digital-buffers-are-essential-in-circuit/A buffer outputs its input unchanged — yet without it, clock trees and shared data buses cannot exist. Covers fan-out, tri-state, and bus contention.Tue, 13 Jan 2026 00:00:00 GMTbuffertri-statefan-outsignal-integritydennyhttps://digisim.io/blog/the-xnor-gate-champion-of-equality-in-digital-logic/https://digisim.io/blog/the-xnor-gate-champion-of-equality-in-digital-logic/The XNOR gate outputs 1 only when its inputs are identical. It is the equality detector behind every magnitude comparator, combination lock, and parity check.Tue, 13 Jan 2026 00:00:00 GMTxnor-gateequality-detectioncomparatorslogic-gateserror-detectiondennyhttps://digisim.io/blog/the-xor-gate-mastering-the-logic-of-difference-for-digital/https://digisim.io/blog/the-xor-gate-mastering-the-logic-of-difference-for-digital/The XOR gate outputs 1 when its inputs differ. It's the core of binary addition, parity checking, controllable inversion in subtractors, and the one-time pad.Tue, 13 Jan 2026 00:00:00 GMTxor-gatearithmetic-circuitscryptographyerror-detectiondennyhttps://digisim.io/blog/visualizing-logic-mastering-karnaugh-maps-for-efficient/https://digisim.io/blog/visualizing-logic-mastering-karnaugh-maps-for-efficient/A Karnaugh map arranges a truth table on a Gray-coded grid where adjacent 1s group into minimal SoP terms, replacing algebra with visual pattern recognition.Tue, 13 Jan 2026 00:00:00 GMTkarnaugh-mapscircuit-optimizationcombinational-logicdennyhttps://digisim.io/blog/xor-vs-xnor-the-critical-difference-in-error-detection/https://digisim.io/blog/xor-vs-xnor-the-critical-difference-in-error-detection/XOR detects difference; XNOR confirms equality. Multi-input chains form odd- and even-parity detectors. Includes a step-by-step 4-bit parity-check build.Tue, 13 Jan 2026 00:00:00 GMTxor-gatexnor-gateerror-detectiondennyhttps://digisim.io/blog/your-first-5-minutes-with-digisim-io-a-beginners-journey/https://digisim.io/blog/your-first-5-minutes-with-digisim-io-a-beginners-journey/Build three starter circuits in DigiSim.io: a switch-and-light, an AND gate, and a multi-gate alarm. No installs, no prerequisites — only a browser needed.Tue, 13 Jan 2026 00:00:00 GMTbeginners-guidedigisim-workflowdigital-logic-101dennyhttps://digisim.io/blog/mastering-binary-addition-building-a-4-bit-ripple-carry/https://digisim.io/blog/mastering-binary-addition-building-a-4-bit-ripple-carry/A 4-bit ripple carry adder chains four full adders to add multi-bit numbers. Covers architecture, propagation delay, overflow detection, and a build.Mon, 12 Jan 2026 00:00:00 GMTripple-carry-adderbinary-additionfull-adderarithmetic-circuitsdennyhttps://digisim.io/blog/mastering-shift-registers-from-serial-to-parallel-conversion/https://digisim.io/blog/mastering-shift-registers-from-serial-to-parallel-conversion/Shift registers chain D flip-flops to move data one bit per clock pulse. Build SIPO, PISO, and PIPO variants and learn how UART and LED matrix drivers use them.Mon, 12 Jan 2026 00:00:00 GMTshift-registersserial-paralleld-flip-flopdata-conversiondennyhttps://digisim.io/blog/logic-gate-truth-tables-your-essential-reference-guide/https://digisim.io/blog/logic-gate-truth-tables-your-essential-reference-guide/A complete truth-table reference for AND, OR, NOT, NAND, NOR, XOR, and XNOR — with Boolean expressions, universal-gate proofs, and CPU applications.Sun, 11 Jan 2026 00:00:00 GMTtruth-tableslogic-gatesreference-guideuniversal-gatesdennyhttps://digisim.io/blog/mastering-sum-of-products-sop-your-guide-to-boolean-function/https://digisim.io/blog/mastering-sum-of-products-sop-your-guide-to-boolean-function/Sum of Products (SOP) converts a truth table to a Boolean expression by ORing minterms. The result maps directly to AND-OR or NAND-NAND hardware.Sun, 11 Jan 2026 00:00:00 GMTsum-of-productsboolean-algebramintermscircuit-designdennyhttps://digisim.io/blog/the-sr-latch-unpacking-the-fundamental-building-block-of/https://digisim.io/blog/the-sr-latch-unpacking-the-fundamental-building-block-of/The SR latch is the simplest bistable circuit. Covers cross-coupled NOR and NAND implementations, the forbidden state, and its role in flip-flops and SRAM.Sun, 11 Jan 2026 00:00:00 GMTsr-latchsequential-logicdigital-memorynor-gatedennyhttps://digisim.io/blog/maxwells-demon-the-19th-century-ghost-that-revealed-the/https://digisim.io/blog/maxwells-demon-the-19th-century-ghost-that-revealed-the/Maxwell's Demon, an 1867 thought experiment, was finally exorcised by Landauer's Principle: erasing one bit dissipates at least kT·ln(2) of heat.Fri, 26 Sep 2025 00:00:00 GMTinformation-theorythermodynamicsmaxwells-demonphysicsdennyhttps://digisim.io/blog/the-3-500-year-journey-of-binary-from-ancient-echoes-to-the/https://digisim.io/blog/the-3-500-year-journey-of-binary-from-ancient-echoes-to-the/Binary is not a 20th-century invention. Egyptian scribes, the I Ching, Pingala, Leibniz, Boole, and Shannon each rediscovered the same primal duality.Tue, 23 Sep 2025 00:00:00 GMTbinaryhistorycomputing-historydenny