Computer Science Fundamentals - Discrete Math Part 1

The smallest unit of data in a computer, representing either a 0 or a 1.

A group of 8 bits, forming a fundamental unit for storing data.

A unit of data processed by a computer, typically consisting of 16, 32, or 64 bits.

The number of different values that can be represented using a specific number of bits.

A numerical system using a base of 2, where each digit is either a 0 or a 1.

The process of converting a number from one numerical system to another.

Operations performed on numbers, including addition, subtraction, multiplication, and division.

The accuracy of representation for a number, often limited by the number of bits used.

A number system where each digit represents a power of 8.

Each digit in an octal number represents a power of 8, starting from 8^0 for the rightmost digit and increasing to the left.

The final value of an octal number is calculated by multiplying each digit with its corresponding weight and summing the results.

A number system where each digit represents a power of 16.

Each digit in a hexadecimal number represents a power of 16, starting from 16^0 for the rightmost digit and increasing to the left.

The final value of a hexadecimal number is calculated by multiplying each digit with its corresponding weight and summing the results.

The number of digits used to represent a number in a particular radix system.

Decimal numbers use powers of 10 as weights for each digit.

Binary numbers use powers of 2 as weights for each digit.

The process of converting a binary number to a decimal number by adding the weights of the digits that are equal to 1.

Octal numbers use powers of 8 as weights for each digit.

Hexadecimal numbers use powers of 16 as weights for each digit.

The point that separates the integer and fractional parts of a number in a radix system.

The base or foundation of a number system, determining the number of unique symbols used to represent values.

The process of converting an n-adic number (base-n) to a decimal number (base-10).

The process of converting a decimal number (base-10) into an n-adic number (base-n).

A number that cannot be represented with a finite number of digits in a given base.

When converting a decimal fraction into an n-adic system, the calculation may result in an infinite repeating decimal.

Computers often handle non-terminating fractions as approximate values due to limitations in representing infinite precision.

Sometimes, converting between bases can be simplified by converting to binary first, then to the desired base (octal or hexadecimal).

The process of converting a decimal number to its binary equivalent by dividing the decimal number repeatedly by 2 and collecting the remainders in reverse order.

The process of converting the fractional part of a decimal number to its binary equivalent by continuously multiplying the fraction by 2 and collecting the integer parts of the results.

A tabular method for converting a decimal number to binary by listing the powers of 2 in descending order and subtracting the largest power that fits into the decimal number, then repeating the process with the remaining value.

The smallest power of 2 that can be subtracted from the decimal number.

The process of removing the largest power of 2 that fits into the decimal number, leaving a new value to work with.

The remaining value after subtracting the largest power of 2.

A binary number that represents the decimal value. It is formed by combining the 1s and 0s placed under the powers of 2 that were subtracted.

A set of powers of 2 arranged in descending order, starting with 2^0 (1).

In the context of number systems, the radix refers to the base of the number system. It determines the number of unique digits used to represent numbers within that system. For example, the decimal system (base 10) uses ten digits (0-9), while the binary system (base 2) uses only two digits (0 and 1).

The process of converting a number from one number system to another. It involves changing the representation of the same value using different bases.

A method for performing multiplication in hexadecimal numbers. It involves the same principle as decimal multiplication, but uses the base 16 instead of the base 10. The carry-over rule is also applied, where any quotient exceeding the base (16) is added to the next operand.

A method for performing addition in binary numbers. It involves the same principle as decimal addition, but uses the base 2 instead of the base 10. The rule is that 1+1=10, meaning a carry-over.

A method for performing subtraction in binary numbers. It involves the same principle as decimal subtraction, but uses the base 2 instead of the base 10. It requires borrowing from higher order bits.

A method for performing addition in octal numbers. It involves the same principle as decimal addition, but uses the base 8 instead of the base 10. The carry-over rule is also applied, where any sum exceeding the base (8) is added to the next operand.