Binary Codes and Number System
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This document summarizes key concepts in digital systems and binary numbers. It discusses why digital systems are preferred over analog, how to convert between number bases, signed and complement number representations, overflow, binary and decimal codes, BCD addition, Gray code, and parity checks. Digital systems are more cost effective, reliable, programmable and selective compared to analog. Number conversions involve grouping bits or dividing decimals. Signed number systems use complement representations to indicate positive and negative values.
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- 3. Why Digital Over Analog ? 1. Reduced Cost 2. More Reliable 3. Programmable (so has major application) 4. Selective ( Akin to a Research Scientist vs a Payroll Schedule) 5. Implemented via Electronic Components
- 4. Number Conversions Convert From X ---- > Y Method Any System(r) To Decimal Multiply Coefficients before Decimal by r ^ index. And Coefficients after Decimal by r^(- index) where index starts from -1 after decimal and 0 before. Decimal to Any System (r) Divide Decimal by r Repeatedly and Collect remainders. The Final Answer is From Last Remainder Collected to First. Binary To Octal Group in 3s Binary To Hexadecimal Group in 4s
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- 6. Complements of Numbers Complements Radix Complement (r^n- N ) Diminished Radix Complement ((r^n-1)-N ) 2โs , 10โs 1โs , 9โs
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