Solution
... Define a minimum length binary code. What is the minimum Hamming distance between any pair of codes? (b) Define a minimum length binary code such that any single-bit error can be detected. What is the Hamming distance between any pair of codes? Answer: (a) For four symbols, we need a two-bit code, w ...
... Define a minimum length binary code. What is the minimum Hamming distance between any pair of codes? (b) Define a minimum length binary code such that any single-bit error can be detected. What is the Hamming distance between any pair of codes? Answer: (a) For four symbols, we need a two-bit code, w ...
Exploring Mathematics Through Problem Solving, Part I
... For many generations, prime numbers have always had mystical and magical appeals to mathematicians. Dating back to Euclid’s days, he had already proved that there are infinitely many prime numbers. However, from what we had seen before, it is very difficult to prove even some of the simple properti ...
... For many generations, prime numbers have always had mystical and magical appeals to mathematicians. Dating back to Euclid’s days, he had already proved that there are infinitely many prime numbers. However, from what we had seen before, it is very difficult to prove even some of the simple properti ...
1.2-1.3 2015 Simplifying algebraic expressions
... HW - Go through expression solving ppt attached to website ...
... HW - Go through expression solving ppt attached to website ...
CMSC 203 / 0202 Fall 2002
... Matrix arithmetic, products Identity matrix Transpose At, symmetric matrices Zero-one matrix, join (), meet (), Boolean product ...
... Matrix arithmetic, products Identity matrix Transpose At, symmetric matrices Zero-one matrix, join (), meet (), Boolean product ...
Math Grade6 Instructional Map 2011-2012
... MG 1.1 Understand the concept of a constant such as ; know the formulas for the circumference and area of a circle. (2) MG 1.2 Know common estimates of (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. (2) MG 1 ...
... MG 1.1 Understand the concept of a constant such as ; know the formulas for the circumference and area of a circle. (2) MG 1.2 Know common estimates of (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. (2) MG 1 ...
x - NYU Computer Science
... • Generalized Pigeonhole Principle: For any function f : X Y acting on finite sets, if n(X) > k * N(Y), then there exists some y from Y so that there are at least k + 1 distinct x’s so that f(x) =y • “If n pigeons fly into m pigeonholes, and, for some positive k, m >k*m, then at least one pigeonho ...
... • Generalized Pigeonhole Principle: For any function f : X Y acting on finite sets, if n(X) > k * N(Y), then there exists some y from Y so that there are at least k + 1 distinct x’s so that f(x) =y • “If n pigeons fly into m pigeonholes, and, for some positive k, m >k*m, then at least one pigeonho ...
Binary Numbers - Computer Science
... The decimal number 3 in binary is 11, but using a fixed size of 8 bits it would be represented as 00000011 Try adding the binary numbers using a fixed size of 8 bits: ...
... The decimal number 3 in binary is 11, but using a fixed size of 8 bits it would be represented as 00000011 Try adding the binary numbers using a fixed size of 8 bits: ...
Chapter 2
... Explore the problem (read the whole thing) Plan the solution (write the equation) Solve the problem Check the solution (does it make sense?) ...
... Explore the problem (read the whole thing) Plan the solution (write the equation) Solve the problem Check the solution (does it make sense?) ...
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.