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About This Tool
Master digital logic, digital communications, and rotary encoder math with the Ubify Gray Code & BCD Studio.
Included Engineering Modules: ā¢ Binary ā Gray Code: Convert pure binary to reflected Gray code and vice-versa with step-by-step XOR mathematical derivations. ā¢ Decimal ā BCD (8421): Convert base-10 integers to Binary Coded Decimal with interactive 4-bit nibble visualization. ā¢ Bitwise Logic Lab: Test AND, OR, XOR, NOT, NAND, NOR, XNOR, Shift Left, and Shift Right on binary operands. ā¢ 4-Bit Truth Table: Interactive matrix comparing Decimal (0-15), Pure Binary, Gray Code, and BCD.
Why Gray Code Matters: In digital hardware and rotary shaft encoders, natural binary transitions often change multiple bits simultaneously (e.g. 0111 to 1000 changes all 4 bits), risking spurious error states during mechanical switching. Gray code guarantees only a single bit changes between consecutive numbers, eliminating race conditions.
How to Use
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Choose a module: Gray Code, BCD 8421, Bitwise Lab, or Truth Table.
- 2
Enter your binary or decimal inputs.
- 3
Inspect the instant conversion along with step-by-step XOR bit-by-bit derivations.
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Copy output values or study consecutive bit transitions in the truth table.
Frequently Asked Questions
What is the formula to convert Binary to Gray code?
The formula is Gray = Binary XOR (Binary >> 1). Each Gray bit is the XOR sum of the current binary bit and the bit to its left.
What is BCD 8421?
BCD (Binary Coded Decimal) encodes each individual decimal digit (0-9) as a separate 4-bit binary nibble weighted 8, 4, 2, and 1.
Is this studio suitable for university engineering coursework?
Yes! The step-by-step proof derivations and bitwise truth tables are built specifically for computer architecture and electrical engineering students.