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Digital Logic Gate & Circuit Simulator

Interactive digital logic circuit simulator covering basic gates (AND, OR, NOT), universal gates (NAND, NOR), Half/Full Adders, and real-time truth tables.

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Preset:

Half Adder Circuit

Adds two single binary bits to produce a Sum (S = A ⊕ B) and Carry (C = A · B).

1. Tap Input Switches (0 or 1):HIGH = 1 (Active) • LOW = 0 (Off)

2. Computed Circuit Outputs & LEDs:

Sum (যোগফল)A ⊕ B

Carry (হাতে থাকা)A · B

Real-Time Truth Table

Active Row Highlighted

A	B	Sum (S)	Carry (C)
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Formula & Derivation

Theoretical foundation, dimensional analysis, and governing boundary conditions.

Boolean Algebra & Combinational Logic Principles

Modern central processing units execute billions of arithmetic operations per second by cascading combinational logic gates switching between 0V (logic 0) and +5V (logic 1).

Half Adder Equations:

Sum: S = A ⊕ B

Carry: C = A · B

Full Adder Equations:

Sum: S = A ⊕ B ⊕ Cin

Cout = (A · B) + (Cin · (A ⊕ B))

Solved Textbook Examples

Three fully worked pedagogical exemplars: standard textbook, advanced edge-case, and authentic past board examination.

Foundational Gatebg-emerald-500/10 text-emerald-400 border border-emerald-500/20

Determine the output of a 2-input XOR gate when inputs are A = 1 and B = 1.

Given Parameters:

Inputs: A = 1, B = 1
Gate: XOR

Procedural Solution:

Boolean definition: Y = A ⊕ B = A'B + AB'.

Substitute values: (0 · 1) + (1 · 0) = 0 + 0 = 0.

An XOR gate outputs 0 whenever both inputs are identical.

Final Answer:Output Y = 0

Secondary Board Standardbg-cyan-500/10 text-cyan-400 border border-cyan-500/20

Calculate the Sum and Carry generated by a Half Adder when adding two binary bits 1 and 1.

Given Parameters:

Operands: A = 1, B = 1

Procedural Solution:

Binary arithmetic: 1 + 1 = 10 in base-2 (decimal 2).

Sum bit: S = A ⊕ B = 1 ⊕ 1 = 0.

Carry bit: C = A · B = 1 · 1 = 1.

Final Answer:Sum (S) = 0, Carry (C) = 1 (Binary: 10₂)

Universal Gate Implementationbg-purple-500/10 text-purple-400 border border-purple-500/20

Demonstrate how an OR gate can be constructed using only universal NAND gates.

Given Parameters:

Target gate: OR
Available: 2-input NAND gates

Procedural Solution:

Apply De Morgan: A + B = ((A + B)')' = (A' · B')'.

Invert input A using NAND(A, A) to get A'.

Invert input B using NAND(B, B) to get B'.

Feed A' and B' into a third NAND to yield A + B.

Final Answer:Exactly 3 NAND gates implement an OR function.

Board Exam & Laboratory Checklist

✓ একক রূপান্তর (SI Units)Convert all inputs to SI units prior to calculation.

✓ সূত্র ও পক্ষান্তর উল্লেখExplicitly isolate target variable before substitution.

✓ তাৎপর্যপূর্ণ অঙ্ক ও রাউন্ডিংPreserve required precision without premature truncation.

Practical Applications

How this scientific principle drives chemical engineering, aerospace, medicine, and research.

From arithmetic logic units (ALUs) inside mobile chipsets to hardware encryption coprocessors and field-programmable gate arrays (FPGAs), these fundamental logic circuits are the bedrock of computing. Toggling switches in this live visualizer lets students ground abstract classroom truth tables in tangible circuit physics.

Frequently Asked Questions

Answers to common conceptual misconceptions and board examination guidelines.

Why are NAND and NOR classified as universal gates?▼

NAND and NOR gates are universal because any Boolean function and all basic gates (AND, OR, NOT) can be synthesized exclusively using networks of either NAND or NOR gates alone.

What differentiates a Half Adder from a Full Adder?▼

A Half Adder adds two single bits producing Sum and Carry. A Full Adder adds three bits (including an incoming Carry-in from a previous stage). Two Half Adders and an OR gate form a Full Adder.

How can logic operations be executed on a physical Casio calculator?▼

On Casio fx-991EX or fx-991CW, navigate to Base-N mode. Press OPTN or LOGIC to access bitwise AND, OR, XOR, and NOT operations directly on binary or hex numbers.