Fixed-Point Arithmetic: An Introduction
... them (at first glance, anyway) as positive integers (i.e., the natural binary representation, defined in the next section). However, the meaning of an N-bit binary word depends entirely on its interpretation, i.e., on the representation set and the mapping we choose to use. In this section, we consi ...
... them (at first glance, anyway) as positive integers (i.e., the natural binary representation, defined in the next section). However, the meaning of an N-bit binary word depends entirely on its interpretation, i.e., on the representation set and the mapping we choose to use. In this section, we consi ...
Slide 1
... This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish t ...
... This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish t ...
ramanujan
... is a house in between (let us call it x) such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. If n is between 50 and 500, what are n and x? Ramanujan did not merely answer the problem but gave the answer with a twist: he gave a continued fractio ...
... is a house in between (let us call it x) such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. If n is between 50 and 500, what are n and x? Ramanujan did not merely answer the problem but gave the answer with a twist: he gave a continued fractio ...
MTH4110/MTH4210 Mathematical Structures
... [The sum of the series a + ar + ar2 + · · · is a/(1 − r) if |r| < 1. In our case a = 9/10 and r = 1/10.] It is important to recall what this means. The sum of an infinite series is a limit; in this case, the sum of any finite number of terms will fall slightly short of the limit, but the difference ...
... [The sum of the series a + ar + ar2 + · · · is a/(1 − r) if |r| < 1. In our case a = 9/10 and r = 1/10.] It is important to recall what this means. The sum of an infinite series is a limit; in this case, the sum of any finite number of terms will fall slightly short of the limit, but the difference ...
Chapter 4 Set Theory
... “A set is a Many that allows itself to be thought of as a One.” (Georg Cantor) In the previous chapters, we have often encountered ”sets”, for example, prime numbers form a set, domains in predicate logic form sets as well. Defining a set formally is a pretty delicate matter, for now, we will be hap ...
... “A set is a Many that allows itself to be thought of as a One.” (Georg Cantor) In the previous chapters, we have often encountered ”sets”, for example, prime numbers form a set, domains in predicate logic form sets as well. Defining a set formally is a pretty delicate matter, for now, we will be hap ...
LOTTARIO Game Conditions
... (a) five numbers, in which case a player shall be deemed to have selected those five numbers with the 40 remaining numbers as the sixth number, and to have 40 6-number selections; or, (b) seven numbers, in which case a player shall be deemed to have seven 6-number selections; or, (c) eight numbers, ...
... (a) five numbers, in which case a player shall be deemed to have selected those five numbers with the 40 remaining numbers as the sixth number, and to have 40 6-number selections; or, (b) seven numbers, in which case a player shall be deemed to have seven 6-number selections; or, (c) eight numbers, ...
1-1 Using Variables
... work multiplied by 6.5. In the table at the bottom left, the variable h stands for the number of hours you worked. A variable is a symbol, usually a letter, that represents one of more numbers. The expression 6.50h is an algebraic expression. An algebraic expression is a mathematical phrase that can ...
... work multiplied by 6.5. In the table at the bottom left, the variable h stands for the number of hours you worked. A variable is a symbol, usually a letter, that represents one of more numbers. The expression 6.50h is an algebraic expression. An algebraic expression is a mathematical phrase that can ...
Recurrences A recurrence relation for a sequence is an
... A password contains letters and numbers with at least 1 letter and 1 number. How many passwords of length 8 are there? A password of length n can be formed by: Any letter or number followed by a length n−1 password. Any number followed by n − 1 letters. Any letter followed by n − 1 numbers. Recurren ...
... A password contains letters and numbers with at least 1 letter and 1 number. How many passwords of length 8 are there? A password of length n can be formed by: Any letter or number followed by a length n−1 password. Any number followed by n − 1 letters. Any letter followed by n − 1 numbers. Recurren ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.