Question 1

How does binary-to-Gray conversion work?

Accepted Answer

Gray code (also called reflected binary) is generated from a normal binary number by XORing each bit with the bit to its left: gᵢ = bᵢ ⊕ bᵢ₊₁. The most-significant bit is copied unchanged. The result is a code where successive values differ by exactly one bit, which is why Gray code is used in rotary encoders, Karnaugh maps, and error-reduction schemes.

Question 2

How does Gray-to-binary conversion reverse it?

Accepted Answer

To recover the binary value, you do a prefix-XOR: starting from the MSB (which is copied), each binary bit bᵢ = gᵢ ⊕ bᵢ₊₁ — that is, XOR the Gray bit with the previously-computed binary bit. The tool shows this as a step table so you can follow each XOR. Both directions also support decimal input/output and any bit width with zero-padding.

Question 3

What is the Gray code sequence generator?

Accepted Answer

Given n bits, the generator produces all 2ⁿ values from 0 to 2ⁿ−1 in Gray-code order, highlighting the single bit that flips between successive entries. You can verify the single-bit-change property (including the wrap from the last value back to the first), and view a complete truth table mapping index → binary → Gray → changed-bit.

Question 4

What are n-ary and balanced Gray codes?

Accepted Answer

N-ary Gray code generalises the binary version to base-r digits — each successive value differs in exactly one digit by ±1, useful for non-binary sensors. Balanced Gray code is a special reflected Gray code where each bit position toggles roughly the same number of times across a full cycle (within ±1 of the average), which is important when each bit flip has a wear or signal cost. The tool generates both.

Question 5

What extra features does this tool have compared to other Gray code converters?

Accepted Answer

(1) Binary → Gray with XOR step table. (2) Gray → binary with prefix-XOR step table. (3) Decimal input/output alongside binary. (4) Selectable bit width with zero-padding. (5) n-bit sequence generator (0…2ⁿ−1) with single-bit-change highlight. (6) Wrap-around single-bit-change verification. (7) N-ary Gray code (any base r ≥ 2). (8) Balanced Gray code generator. (9) Truth-table view. (10) BigInt support for wide values (up to 2ⁿ−1 where n ≤ 53 safely, larger via BigInt). (11) History (localStorage, last 20). (12) Shareable URL. 100% client-side and offline — your data never leaves the device.

Gray Code Converter (Binary ↔ Gray, Sequence, N-ary, Balanced)

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