Number Systems and Conversions

Study Notes

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)

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

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

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.

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.

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.

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.