--- title: "Digital signal and Gray code" subject: "Digital Logic" chapter: 1 key: "semester_3/digital_logic:digital-signal-gray-code" source: https://www.bctengineer.com/q/semester_3/digital_logic/digital-signal-gray-code site: BCT Engineering --- # Digital signal and Gray code Digital Logic · Chapter 1: Introduction - Asked in: 2070 Chaitra, 1+5 marks - Video: [Lec-9: Binary to Gray Code Conversion & Vice-versa](https://www.youtube.com/watch?v=R7uuIACpdGQ) — Gate Smashers - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/digital_logic/digital-signal-gray-code - Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1 ## Question Define digital signal and explain Gray code with example. ## Short answer A digital signal has discrete levels (typically 0 and 1) that change at discrete times. Gray code is an unweighted reflected binary code where consecutive numbers differ by one bit; e.g., binary 1101 → Gray 1011. Used in encoders and K-maps. ## Answer #### Digital signal A **digital signal** is a signal that has only a finite number of discrete values (usually two levels, 0 and 1) and changes at discrete instants of time. Example: clock pulses and data in a computer. #### Gray code **Gray code** is an unweighted binary code in which **two consecutive numbers differ in only one bit**. It is also called the **reflected binary code**, because the code for $n$ bits is built by writing the $(n-1)$-bit code, reflecting it like a mirror, and prefixing 0 to the top half and 1 to the bottom half. ```text 1-bit 2-bit 3-bit 0 00 000 1 01 001 --- 11 011 mirror 10 010 ---- 110 mirror 111 101 100 ``` | Decimal | Binary | Gray | |---|---|---| | 0 | 000 | 000 | | 1 | 001 | 001 | | 2 | 010 | 011 | | 3 | 011 | 010 | | 4 | 100 | 110 | | 5 | 101 | 111 | | 6 | 110 | 101 | | 7 | 111 | 100 | **Binary to Gray**: keep the MSB; $G_i = B_{i+1} \oplus B_i$. Example: $(1101)_2$ → 1, 1⊕1 = 0, 1⊕0 = 1, 0⊕1 = 1 → $(1011)_{Gray}$. **Gray to binary**: keep the MSB; $B_i = B_{i+1} \oplus G_i$. Example: $(1011)_{Gray}$ → 1, 1⊕0 = 1, 1⊕1 = 0, 0⊕1 = 1 → $(1101)_2$. **Features and uses** - Unweighted, so not used for arithmetic. - Only one bit changes per step, so it avoids false readings in rotary shaft encoders. - Used to label K-map rows and columns (00, 01, 11, 10). - Used in ADCs and low-power counters. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is a digital signal? A. One that varies continuously B. One with a finite number of discrete values, usually 0 and 1 C. One that only has positive values D. One that is always high Answer: B. Digital signals change at discrete instants between discrete levels. (Key point: Digital signal) 2. Why is Gray code called reflected binary code? A. Its bits are reversed in order B. It repeats the same codes twice C. The n-bit code is the (n-1)-bit code mirrored with 0 prefixed to the top half and 1 to the bottom half D. It is the inverse of binary Answer: C. Reflection builds the sequence step by step. (Key point: Reflected code) 3. What is (1011) Gray in binary? A. 1011 B. 1110 C. 0100 D. 1101 Answer: D. 1; 1^0=1; 1^1=0; 0^1=1. (Key point: Gray to binary) 4. Which is a use of Gray code? A. K-map labelling (00, 01, 11, 10) B. Decimal arithmetic C. Character storage D. Weighted addition Answer: A. Adjacent cells differ by one bit. (Key point: Uses) ## Close variants set in other exams - [Digital IC signal levels and Gray code](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aic-signal-levels-gray-code) — Digital Logic, chapter 1, asked 2× ## Related in Digital Logic - [Digital/analog signals, Gray and Excess-3 codes](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Adigital-analog-gray-excess3) — Digital Logic, chapter 1 - [Gray code with examples](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-code-explain) — Digital Logic, chapter 1, asked 3× - [3-bit Gray code synchronous counter](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-code-sync-counter-3bit) — Digital Logic, chapter 8, asked 2× - [BCD code and 3-bit binary-to-Gray converter](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Abcd-code-gray-converter) — Digital Logic, chapter 1 - [Gray code and 3-bit binary-to-Gray converter](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-code-binary-gray-converter) — Digital Logic, chapter 1 - [Gray vs binary code, convert (10110)₂ to Gray](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-vs-binary-convert-10110) — Digital Logic, chapter 1