"use strict"; const {jsx: _jsx} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { code: "code", pre: "pre", ..._provideComponents(), ...props.components }; return _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-mdx", children: "\n\n---\n\n\n ### 📇 Revision Cards\n\n #### 📌 1.1 — Number Systems & Conversions\n\n | | |\n |---|---|\n | **Concept** | Different number systems (Binary, Octal, Decimal, Hexadecimal) and methods to convert between them. |\n | **Key Point** | Each number system has a base (radix) $r$, with digits $0$ to $r-1$. Conversion involves repeated division or multiplication by the base. |\n | **Exam Angle** | 4 marks — Convert numbers across all four systems; may include fractional conversions. |\n\n #### 📌 1.2 — Binary Arithmetic\n\n | | |\n |---|---|\n | **Concept** | Performing addition, subtraction, multiplication, and division on binary numbers. |\n | **Key Point** | Binary addition rules: $0+0=0,\\;0+1=1,\\;1+0=1,\\;1+1=0$ with carry 1. Subtraction uses borrow. |\n | **Exam Angle** | 2 marks — Perform binary addition or subtraction; may include overflow detection. |\n\n #### 📌 1.3 — Subtraction using 1's & 2's Complement\n\n | | |\n |---|---|\n | **Concept** | Subtract binary numbers by adding the complement of the subtrahend, simplifying hardware implementation. |\n | **Key Point** | 1's complement: Invert all bits, add result to minuend. 2's complement: 1's complement +1, then add. Discard final carry in 2's complement. |\n | **Exam Angle** | 4 marks — Solve subtraction using both complement methods; indicate sign of result. |\n\n #### 📌 1.4 — Codes (BCD, Gray, Excess-3, ASCII)\n\n | | |\n |---|---|\n | **Concept** | Binary codes used to represent decimal digits, minimize errors, and encode alphanumeric characters. |\n | **Key Point** | BCD: 4-bit code for digits 0–9; **Gray**: only one bit changes between successive values; **Excess-3**: BCD +3; **ASCII**: 7/8-bit alphanumeric code. |\n | **Exam Angle** | 4 marks — Code conversions (Gray to Binary, BCD to Excess-3, etc.) and applications of each code. |\n\n #### 📌 1.5 — BCD Arithmetic\n\n | | |\n |---|---|\n | **Concept** | Performing addition and subtraction on BCD numbers with correction logic and complement methods. |\n | **Key Point** | BCD addition: Add binary, if sum > 9 add 6 correction. BCD subtraction: Use 9's or 10's complement. |\n | **Exam Angle** | 4 marks — BCD addition with correction; subtract using 9's or 10's complement. |\n\n ---\n\n ### 📝 Key Terms\n\n \n \n The number of unique digits used in a number system. E.g., Binary: 2, Decimal: 10, Hexadecimal: 16.\n Kisi bhi number system mein upalabdh unique digits ki sankhya. Jaise, Binary: 2, Decimal: 10, Hexadecimal: 16.\n \n \n Inverting all bits of a binary number (0 → 1, 1 → 0).\n Binary number ke sabhi bits ko invert karna (0 → 1, 1 → 0).\n \n \n 1's complement + 1; standard method for representing signed binary numbers.\n 1's complement mein 1 jodna; signed binary numbers ko represent karne ka standard method.\n \n \n Each decimal digit (0–9) is represented by its 4-bit binary equivalent.\n Har decimal digit (0–9) ko uske 4-bit binary equivalent dwara represent kiya jata hai.\n \n \n Code where successive values differ by exactly one bit; used in error detection and Karnaugh maps.\n Ek code jisme successive values ke beech sirf ek bit change hota hai; error detection aur K-maps mein upyog hota hai.\n \n \n BCD code with 3 added to each digit; self-complementing property simplifies subtraction.\n BCD code jisme har digit mein 3 joda jata hai; self-complementing property subtraction ko saral banati hai.\n \n \n American Standard Code for Information Interchange; 7-bit (or 8-bit with parity) code for text characters.\n American Standard Code for Information Interchange; text characters ke liye 7-bit (ya 8-bit parity ke saath) code.\n \n \n\n ### ⚠️ Common Mistakes to Avoid\n\n \n \n **Mistake 1:** Forgetting to add the end-around carry when using 1's complement subtraction. \n **Correct Approach:** After adding the 1's complement, always check for a carry out of the most significant bit; if present, add it back (end-around carry).\n\n **Mistake 2:** Adding correction (6) in BCD addition even when the binary sum is ≤ 9. \n **Correct Approach:** Add 6 only if the sum is greater than 9 or if a carry occurred from the lower nibble.\n\n **Mistake 3:** Confusing Gray code with binary; generating Gray code incorrectly. \n **Correct Approach:** The first bit remains the same; for each subsequent bit, XOR the previous binary bit with the current binary bit.\n \n \n **Mistake 1:** 1's complement subtraction mein end-around carry jodna bhool jana. \n **Correct Approach:** 1's complement jodne ke baad, hamesha most significant bit se carry check karein; agar hai toh use wapas jodein (end-around carry).\n\n **Mistake 2:** BCD addition mein tab bhi correction (6) jodna jab binary sum ≤ 9 ho. \n **Correct Approach:** Correction sirf tab jodein jab sum 9 se adhik ho ya lower nibble se carry aa raha ho.\n\n **Mistake 3:** Gray code aur binary mein confusion; Gray code galat generate karna. \n **Correct Approach:** Pehla bit same reheta hai; har agle bit ke liye, previous binary bit aur current binary bit ka XOR karein.\n \n \n\n ### 🔗 How This Unit Connects\n\n \n \n **Before this unit, you learned:** Basic arithmetic operations (addition, subtraction) — now applied to binary numbers. \n **This unit is used in:** Unit 2 (Logic Gates & Boolean Algebra) for understanding gate-level operations; Unit 3 (Combinational Circuits) for designing adders, subtractors, and code converters; Unit 4 (Sequential Circuits) for counters and registers that use binary codes.\n \n \n **Is unit se pehle aapne seekha:** Basic arithmetic operations (addition, subtraction) — ab binary numbers par apply karenge. \n **Is unit ka upyog hota hai:** Unit 2 (Logic Gates & Boolean Algebra) mein gate-level operations samajhne ke liye; Unit 3 (Combinational Circuits) mein adders, subtractors, aur code converters design karne mein; Unit 4 (Sequential Circuits) mein counters aur registers jo binary codes upyog karte hain.\n \n \n\n\n\n ### 📇 Revision Cards\n\n #### 📌 1.1 — Number Systems & Conversions\n\n | | |\n |---|---|\n | **Concept** | Alag-alag number systems (Binary, Octal, Decimal, Hexadecimal) aur unke beech conversion ke tarike. |\n | **Key Point** | Har number system ka ek base (radix) $r$ hota hai, digits 0 se $r-1$ tak hote hain. Conversion ke liye base se baar-baar division ya multiplication karte hain. |\n | **Exam Angle** | 4 marks — Charo number systems mein conversion karna; fractional conversions bhi aa sakte hain. |\n\n #### 📌 1.2 — Binary Arithmetic\n\n | | |\n |---|---|\n | **Concept** | Binary numbers par addition, subtraction, multiplication, aur division karna. |\n | **Key Point** | Binary addition ke niyam: $0+0=0,\\;0+1=1,\\;1+0=1,\\;1+1=0$ carry 1 ke saath. Subtraction borrow ka upyog karta hai. |\n | **Exam Angle** | 2 marks — Binary addition ya subtraction karna; overflow detection bhi aa sakta hai. |\n\n #### 📌 1.3 — Subtraction using 1's & 2's Complement\n\n | | |\n |---|---|\n | **Concept** | Binary numbers ko subtract karne ke liye subtrahend ka complement jodna, jisse hardware simple ho jata hai. |\n | **Key Point** | 1's complement: Sab bits invert karein, minuend mein jodein. 2's complement: 1's complement +1, phir jodein. 2's complement mein final carry discard karte hain. |\n | **Exam Angle** | 4 marks — Dono complement methods se subtraction karna; result ka sign batana. |\n\n #### 📌 1.4 — Codes (BCD, Gray, Excess-3, ASCII)\n\n | | |\n |---|---|\n | **Concept** | Binary codes jo decimal digits ko represent karne, errors minimize karne, aur alphanumeric characters encode karne ke liye use hote hain. |\n | **Key Point** | BCD: 0–9 digits ke liye 4-bit code; **Gray**: successive values ke beech sirf 1 bit badalta hai; **Excess-3**: BCD +3; **ASCII**: 7/8-bit alphanumeric code. |\n | **Exam Angle** | 4 marks — Code conversions (Gray to Binary, BCD to Excess-3, etc.) aur har code ke applications. |\n\n #### 📌 1.5 — BCD Arithmetic\n\n | | |\n |---|---|\n | **Concept** | BCD numbers par addition aur subtraction correction logic aur complement methods ke saath karna. |\n | **Key Point** | BCD addition: Binary jodein, agar sum > 9 ho toh 6 correction jodein. BCD subtraction: 9's ya 10's complement use karein. |\n | **Exam Angle** | 4 marks — BCD addition with correction; 9's/10's complement se subtraction karna. |\n\n ---\n\n ### 📝 Key Terms\n\n \n \n\n ### ⚠️ Common Mistakes to Avoid\n\n \n\n ### 🔗 How This Unit Connects\n\n \n\n\n\n\n\n \n\n\n\n \n\n\n\n \n\n\n\n\n### 🗺️ Concept Map\n\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n---\n\n### 📊 Exam Pattern Quick Look\n\n\n | Subtopic | Expected Marks | Question Type | Difficulty |\n |----------|---------------|---------------|------------|\n | 1.1 Number Systems & Conversions | 4 | Convert given numbers, fractional conversion | Medium ⭐⭐ |\n | 1.2 Binary Arithmetic | 2 | Perform addition/subtraction | Easy ⭐ |\n | 1.3 Subtraction using 1's & 2's Complement | 4 | Solve subtraction, indicate sign | Medium ⭐⭐ |\n | 1.4 Codes (BCD, Gray, Excess-3, ASCII) | 4 | Code conversion, explain application | Medium ⭐⭐ |\n | 1.5 BCD Arithmetic | 4 | BCD addition with correction, complement subtraction | Hard ⭐⭐⭐ |\n\n\n---\n\n\n \n \n\n **General Conversion (Integer part):** \n $$ N_{10} = \\sum_{i=0}^{n-1} d_i \\times r^i $$\n\n **Binary to Decimal (Fractional):** \n $$ N_{10} = \\sum_{i=-m}^{-1} d_i \\times r^i $$\n\n **1's Complement:** \n $$ 1's \\; comp = (2^n - 1) - N $$\n\n **2's Complement:** \n $$ 2's \\; comp = 1's \\; comp + 1 = (2^n) - N $$\n\n **BCD Addition Correction:** \n If (Binary Sum) > 9 or (Carry = 1) then add $6_{10} = 0110_2$ to the sum.\n\n **Decimal to Binary (Repeated Division):** \n $$ \\text{Divide by 2, collect remainders from LSB to MSB} $$\n\n \n\n \n - **Base (Radix) identification**: Always check the base before any conversion.\n - **Complement subtraction**: 2's complement is more efficient because it avoids end-around carry.\n - **Gray code generation**: First bit same; subsequent bits = previous binary bit XOR current binary bit.\n - **Excess-3**: Self-complementing property simplifies subtraction (9's complement of Excess-3 is obtained by bitwise inversion).\n - **ASCII**: 7-bit standard; 8-bit with parity for error checking.\n \n\n\n\n \n What is the binary equivalent of $(572.4)_8$?\n \n \n \n \n \n\n \n Subtract $(1101)_2$ from $(1010)_2$ using 2's complement method. What is the result in decimal?\n \n \n \n \n \n\n 9.\" explanation=\"Binary addition of 0111 (7) and 0101 (5) gives 1100 (12). Since 1100 (12) > 9, add 0110 (6) → 1100 + 0110 = 10010. Correct BCD result is 0001 0010 (12).\">\n Add the BCD numbers 0111 (7) and 0101 (5). What is the correct BCD sum?\n \n \n \n \n \n\n \n What is the Gray code equivalent of decimal 9?\n \n \n \n \n \n\n \n What is the Excess-3 code for decimal digit 6?\n \n \n \n \n \n\n" }) }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = { ..._provideComponents(), ...props.components }; return MDXLayout ? _jsx(MDXLayout, { ...props, children: _jsx(_createMdxContent, { ...props }) }) : _createMdxContent(props); } return { default: MDXContent };