Numerical Representations and Number Systems

Study Notes

Quantities can be represented in analog or digital forms.
Analog representation uses a continuously varying physical quantity, such as voltage or current, to represent a value.
Digital representation uses discrete symbols, called digits, to represent values.
Digital systems manipulate information represented in digital form.
Analog systems manipulate information represented in analog form.
Digital systems have advantages over analog systems, including ease of design, higher resolution, greater error/fault tolerance, flexibility, and less noise.

Decimal Number System: Uses base 10 with digits 0-9. (Ex: 7392.15)
Binary Number System: Uses base 2 with digits 0 and 1. (Ex: 11010.11)
Octal Number System: Uses base 8 with digits 0-7. (Ex: 127.4)
Hexadecimal Number System: Uses base 16 with digits 0-9 and A-F. (Ex: B65F).

Binary to Decimal: Multiply each bit by 2 raised to the power of its position (starting from 0 on the right) and add the results.
Decimal to Binary: Repeatedly divide by 2 and keep track of the remainders. The remainders form the binary representation in reverse order.
Octal to Decimal: Multiply each digit by 8 raised to the power of its position and add the results.
Decimal to Octal: Repeatedly divide by 8 and keep track of the remainders.
Hexadecimal to Decimal: Multiply each digit by 16 raised to the power of its position and add the results.
Decimal to Hexadecimal: Repeatedly divide by 16 and keep track of the remainders.
Octal to Binary: Convert each octal digit to its equivalent 3-bit binary representation.
Binary to Octal: Group binary bits in threes, starting from the right, and convert each group to its equivalent octal digit.
Binary to Hexadecimal: Group binary bits in fours, starting from the right, and convert each group to its equivalent hexadecimal digit.
Hexadecimal to Binary: Convert each hexadecimal digit to its equivalent 4-bit binary representation.