Multiplication tableIn mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. The oldest known multiplication tables were used by the Babylonians about 4000 years ago.
Ancient Egyptian multiplicationIn mathematics, ancient Egyptian multiplication (also known as Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication), one of two multiplication methods used by scribes, is a systematic method for multiplying two numbers that does not require the multiplication table, only the ability to multiply and divide by 2, and to add. It decomposes one of the multiplicands (preferably the smaller) into a set of numbers of powers of two and then creates a table of doublings of the second multiplicand by every value of the set which is summed up to give result of multiplication.
Binary-coded decimalIn computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications (e.g. error or overflow). In byte-oriented systems (i.e. most modern computers), the term unpacked BCD usually implies a full byte for each digit (often including a sign), whereas packed BCD typically encodes two digits within a single byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9.
Single-precision floating-point formatSingle-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 231 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2−23) × 2127 ≈ 3.
Complement (set theory)In set theory, the complement of a set A, often denoted by A∁ (or A′), is the set of elements not in A. When all sets in the universe, i.e. all sets under consideration, are considered to be members of a given set U, the absolute complement of A is the set of elements in U that are not in A. The relative complement of A with respect to a set B, also termed the set difference of B and A, written is the set of elements in B that are not in A.
Decimal separatorA decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g. "." in 12.45). Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping. Any such symbol can be called a decimal mark, decimal marker, or decimal sign.
Matrix multiplicationIn mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.
Decimal representationA decimal representation of a non-negative real number r is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator: Here is the decimal separator, k is a nonnegative integer, and are digits, which are symbols representing integers in the range 0, ..., 9. Commonly, if The sequence of the —the digits after the dot—is generally infinite. If it is finite, the lacking digits are assumed to be 0.
Modular arithmeticIn mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.
Elementary arithmeticElementary arithmetic is a branch of mathematics involving basic numerical operations, namely addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and being the foundation of all mathematics, elementary arithmetic is generally the first critical branch of mathematics to be taught in schools. Numerical digit Symbols called digits are used to represent the value of numbers in a numeral system. The most commonly used digits are the Arabic numerals (0 to 9).
Fixed-point arithmeticIn computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals.
Decimal floating pointDecimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base-2) fractions. The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values.
