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DIGITAL LOGIC DESIGN

CHAPTER I

NUMBER SYSTEMS AND

CODES

VIT UNIVERSITY 2

Number systems and codes

• Representation of numbers
• Decimal - Octal - Hexadecimal number

systems

• Representation of negative numbers
• Complement of a number
• Binary arithmetic
• Binary codes for decimal numbers
• Error detecting and correcting codes

VIT UNIVERSITY 4

Number base conversions

• To convert a number in base r to decimal is done by expanding the number in a power series and adding all the terms
• If the number includes a radix point, it is necessary to separate the number k into an integer part and a fraction part.
• Decimal number is converted to number in base r by dividing the number and all successive quotients by r and accumulating the remainders.

Hexadecimal Numbers

Hexadecimal Numbers

• Binary-to-hexadecimal conversion
• Hexadecimal-to-decimal conversion
• Decimal-to-hexadecimal conversion

Hexadecimal Numbers

• Binary-to-hexadecimal conversion
  1. Break the binary number into 4-bit groups
  2. Replace each group with the hexadecimal equivalent

Hexadecimal Numbers

• Decimal-to-hexadecimal conversion
  • Repeated division by 16

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