Lecture Notes on Number Representations, Logarithms, and Algorithms

Vocabulary flashcards based on lecture notes covering number representations, logarithms, polynomial-time algorithms, and modular arithmetic.

Base-10 Representation

Representation of an integer as a sum of powers of 10, e.g., 41025 = 4 * 10^4 + 1 * 10^3 + 0 * 10^2 + 2 * 10^1 + 5 * 10^0

Base-b Representation

A way to represent integers using a base b > 1, where the digits are between 0 and b-1.

Binary Representation

Base 2

Octal Representation

Base 8

Decimal Representation

Base 10

Hexadecimal Representation

Base 16. Uses digits 0-9 and letters A-F to represent values 10-15.

Logarithm

An inverse of an exponential function. logb(x) = y means b^y = x.

Base of Logarithm

The base of the logarithmic function, denoted as b in logb(x).

Polynomial-Time Algorithms

Algorithms with running times that are polynomial functions of the input size, e.g., (input size)^c.

Input Size of Integer m

The number of digits needed to represent m, proportional to log m.

Residue of m modulo n

The remainder when m is divided by n. Written as m mod n.