--- title: "ASCII code and binary-to-Excess-3 converter" subject: "Digital Logic" chapter: 1 key: "semester_3/digital_logic:ascii-binary-excess3-converter" source: https://www.bctengineer.com/q/semester_3/digital_logic/ascii-binary-excess3-converter site: BCT Engineering --- # ASCII code and binary-to-Excess-3 converter Digital Logic · Chapter 1: Introduction - Asked in: 2082 Shrawan, 2+6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/digital_logic/ascii-binary-excess3-converter - Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1 ## Question Define an ASCII code. Design a binary to excess-3 code converter circuit using basic gates. ## Short answer ASCII is a 7-bit code for 128 characters. A BCD-to-excess-3 converter adds 3 (0011) to a 4-bit digit; simplified expressions: W=A+BC+BD, X=B'C+B'D+BC'D', Y=CD+C'D', Z=D'. It uses AND, OR, NOT gates. ## Answer #### ASCII code **ASCII (American Standard Code for Information Interchange)** is a 7-bit alphanumeric code that represents 128 characters: letters, digits, symbols and control characters. Example: 'A' = 65 = 100 0001, 'a' = 97 = 110 0001, '0' = 48 = 011 0000. #### Binary (BCD) to Excess-3 code converter Inputs: 4-bit binary/BCD digit $ABCD$ ($A$ = MSB), valid 0–9. Outputs: Excess-3 code $WXYZ$ = input + 3. Inputs 10–15 never occur, so they are **don't cares (X)**. | Dec | A | B | C | D | W | X | Y | Z | |---|---|---|---|---|---|---|---|---| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | | 2 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | | 3 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | | 4 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | | 5 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | | 6 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | | 7 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | | 8 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | | 9 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | #### K-map simplification Minterms (don't cares $d = 10$–$15$): - $W = \sum m(5,6,7,8,9) + d$ - $X = \sum m(1,2,3,4,9) + d$ - $Y = \sum m(0,3,4,7,8) + d$ - $Z = \sum m(0,2,4,6,8) + d$ K-map for $W$ (rows $AB$, columns $CD$): ```text CD AB 00 01 11 10 00 | 0 | 0 | 0 | 0 | 01 | 0 | 1 | 1 | 1 | 11 | X | X | X | X | 10 | 1 | 1 | X | X | ``` Groups: $A$ (rows 11 and 10), $BD$, $BC$. Simplified expressions: $$ \begin{aligned} W &= A + BC + BD \\ X &= \bar B C + \bar B D + B\bar C\bar D \\ Y &= CD + \bar C\bar D \\ Z &= \bar D \end{aligned} $$ (Each equation can be checked against all ten rows of the truth table.) #### Logic circuit (basic gates) ```text A ----------------------------+ B --+--[AND]-- BC ------------+--[OR]--- W C --+ | B --+--[AND]-- BD ------------+ D --+ B'--+--[AND]-- B'C -----------+ C --+ | B'--+--[AND]-- B'D -----------+--[OR]--- X D --+ | B --+ | C'--+--[AND]-- BC'D' ---------+ D'--+ C --+--[AND]-- CD ------------+--[OR]--- Y D --+ | C'--+--[AND]-- C'D' ----------+ D'--+ D ----[NOT]---------------------------- Z ``` NOT gates generate $\bar B$, $\bar C$ and $\bar D$; the $\bar D$ inverter also drives output Z directly. The circuit therefore uses 7 AND gates, 3 OR gates and 3 NOT gates. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is ASCII? A. An 8-bit weighted BCD code B. A 7-bit alphanumeric code for 128 characters C. A code where successive values differ by one bit D. A 4-bit code for decimal digits Answer: B. ASCII is for text. (Key point: ASCII) 2. Why are inputs 10-15 don't cares in the BCD to XS-3 converter? A. They give zero outputs B. They are inverted C. They never occur as valid BCD digits D. They are the same as 0-5 Answer: C. Don't cares allow bigger K-map groups. (Key point: Don't cares) 3. What is the simplified Z output (LSB)? A. Z = D B. Z = C'D' C. Z = CD D. Z = D' Answer: D. XS-3 LSB is the complement of the BCD LSB. (Key point: Outputs) 4. What is the simplified W (MSB) output? A. W = A + BC + BD B. W = A'BC C. W = AB D. W = BC + CD Answer: A. W is 1 for digits 5 to 9. (Key point: W output) ## Close variants set in other exams - [Excess-3 code and binary-to-Excess-3 converter](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aexcess3-binary-converter) — Digital Logic, chapter 1, asked 2× ## Related in Digital Logic - [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 - [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 - [ASCII code with examples](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aascii-code-explain) — Digital Logic, chapter 1, asked 2× - [Importance of coding and ASCII code](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Acoding-importance-ascii) — Digital Logic, chapter 1 - [Excess-3 code with examples](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aexcess3-code-explain) — Digital Logic, chapter 1, asked 4× ## Related in other subjects - [Excess gain compensation in Sallen-Key circuit](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Asallen-key-excess-gain-compensation) — Filter Design, chapter 6, asked 3×