Number Systems and Conversions

Types of Number Systems

• Decimal Number System: Base 10, uses 10 digits from 0 to 9
• Binary Number System: Base 2, uses 2 digits 0 and 1 (used in computers)
• Octal Number System: Base 8, uses 8 digits from 0 to 7
• Hexadecimal Number System: Base 16, uses 16 digits from 0 to 9 and A to F (used in computer programming)

Number System Conversion

• Binary to Decimal: Each binary digit is multiplied by a power of 2, starting from 2^0
• Decimal to Binary: Divide the decimal number by 2 and keep track of remainders
• Octal to Decimal: Each octal digit is multiplied by a power of 8, starting from 8^0
• Hexadecimal to Decimal: Each hexadecimal digit is multiplied by a power of 16, starting from 16^0

Number System Operations

• Addition: Performed digit by digit, carrying or borrowing as necessary
• Subtraction: Performed digit by digit, borrowing as necessary
• Multiplication: Performed digit by digit, shifting and adding as necessary
• Division: Performed digit by digit, shifting and subtracting as necessary

Number System Applications

• Computer Science: Binary number system is used to represent data and instructions
• Networking: IP addresses are represented in dotted decimal notation (IPv4) or hexadecimal notation (IPv6)
• Cryptography: Number systems are used to develop encryption algorithms and secure data transmission
• Mathematics: Number systems are used to represent and solve mathematical equations and problems

Types of Number Systems

• Base 10 number system uses 10 digits from 0 to 9 and is commonly used in everyday life.
• Base 2 number system uses 2 digits 0 and 1, is used in computers, and is the basis for all computer programming.
• Base 8 number system uses 8 digits from 0 to 7 and is used in some computer programming languages.
• Base 16 number system uses 16 digits from 0 to 9 and A to F, is used in computer programming, and is a more human-readable representation of binary data.

Number System Conversion

• Binary to decimal conversion involves multiplying each binary digit by a power of 2, starting from 2^0.
• Decimal to binary conversion involves dividing the decimal number by 2 and keeping track of remainders.
• Octal to decimal conversion involves multiplying each octal digit by a power of 8, starting from 8^0.
• Hexadecimal to decimal conversion involves multiplying each hexadecimal digit by a power of 16, starting from 16^0.

Number System Operations

• Addition in any number system is performed digit by digit, with carrying or borrowing as necessary.
• Subtraction in any number system is performed digit by digit, with borrowing as necessary.
• Multiplication in any number system is performed digit by digit, with shifting and adding as necessary.
• Division in any number system is performed digit by digit, with shifting and subtracting as necessary.

Number System Applications

• Binary number system is used to represent data and instructions in computer science.
• IP addresses are represented in dotted decimal notation (IPv4) or hexadecimal notation (IPv6) in computer networking.
• Number systems are used to develop encryption algorithms and secure data transmission in cryptography.
• Number systems are used to represent and solve mathematical equations and problems in mathematics.