Which of the following operators will give the remainder after dividing 3 by 2?

A mod B = ( A + K ⋅ B ) mod B A \text K K . It is true that 5 divided by 3 gives you a remainder of 2 However, it is NOT true that -5 divided by 3 gives you a remainder of 2. It gives you a remainder of 1. We can do some long division to prove it: First we'll do the simple 5/3 _1_R2 3 / 5 -3 (Since 1 * 3 = 3) --- 2 We can check our result: 5 = 1 * 3 + 2 Now we can do -5/3 _-2_R1 3 / -5 -(-6) (Since -2 * 3= -6) --- 1 We can check our result: -5 = -2 * 3 + 1 The -2 seems strange since we might think 3 goes into 5, -1 times. But this would make our remainder negative (which is not allowed) Let's see what would happen, if we allowed negative remainders (we don't, but computers do!) it would look like this: _-1_R-2 3 / -5 -(-3) (Since -1 * 3= -3) --- -2 We can check our result: -5 = -1 * 3 + (-2) Notice that if we go 2 steps counter clockwise on the modular circle for 3 that we end up at 1. Notice that if we add one multiple of 3 to -2 we end up at 1. Again, we don't allow negative remainders, but it may give you some intuition for what is going on, and for how congruence modulo works later. Hope this makes sense Johann Carl Friedrich Gauss is usually attributed with the invention/discovery of modular arithmetic. In 1796 he did some work that advanced the field, and in 1801 published the book Disquisitiones Arithmeticae which, amongst other things, introduced congruence modulo and the ≡ symbol. So he is the person that laid out the modern approach to modular arithmetic that we ...

In this article Divides two numbers and returns only the remainder. Syntax result = number1 Mod number2 Parts result Required. Any numeric variable or property. number1 Required. Any numeric expression. number2 Required. Any numeric expression. Supported types All numeric types. This includes the unsigned and floating-point types and Decimal. Result The result is the remainder after number1 is divided by number2. For example, the expression 14 Mod 4 evaluates to 2. Note There is a difference between remainder and modulus in mathematics, with different results for negative numbers. The Mod operator in Visual Basic, the .NET Framework op_Modulus operator, and the underlying The result of a Mod operation retains the sign of the dividend, number1, and so it may be positive or negative. The result is always in the range (- number2, number2), exclusive. For example: Public Module Example Public Sub Main() Console.WriteLine($" 8 Mod 3 = ") End Sub End Module ' The example displays the following output: ' 8 Mod 3 = 2 ' -8 Mod 3 = -2 ' 8 Mod -3 = 2 ' -8 Mod -3 = -2 Remarks If either number1 or number2 is a floating-point value, the floating-point remainder of the division is returned. The data type of the result is the smallest data type that can hold all possible values that result from division with the data types of number1 and number2. If number1 or number2 evaluates to Related operators include the following: • The 14 \ 4 evaluates to 3. • The 14 / 4 evaluates to 3.5. Attempte...

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:Assignment 5.2: Applying Integer Division and Modulus (10 pts) In Java dividing one integer by another truncates the remainder, which removes the decimal part. To compute the integer remainder, we use the remainder operator (%), also known as the modulus operator. The % operator finds the remainder after division of one number by another. The Assignment 5.2: Applying Integer Division and Modulus (10 pts) • In Java dividing one integer by another truncates the remainder, which removes the decimal part. To compute the integer remainder, we use the remainder operator (%), also known as the modulus operator. • The % operator finds the remainder after division of one number by another. The Java expression a % b (pronounced a mod b) returns the remainder of the division of a by b if both numbers are positive. For example: 3 r 1 2 ) 7 -6 1 remainder • For this assignment we will use both the division and remainder operators to extract single digits form an integer number. • Write a program that gets three numbers from the user and then sums: • the hundreds digit of the first number • with the tens digit of the second number and • the unit digit of the third number. • For example, the sum of the diagonal digits of the following three numbers is 3 because the numbers are all 1 on the diagonal as shown by...

Choose the correct answer: Opcode, funct3 and funct7/6 in instruction format are used to... “Since you have posted multiple questions, we will provide the solution only upto three of the specified question as per our Q&A guidelines. Please repost the remaining question by mentioning the required parts that need to be answered.” Introduction: The computer process execution depends on four parts. 1. Fetch: The processor retrieves the next instruction from memory. 2. Decode: The processor decodes the instruction to determine the... Posted29 days ago

In this article The following operators perform arithmetic operations with operands of numeric types: • Unary ++ (increment), -- (decrement), + (plus), and - (minus) operators • Binary * (multiplication), / (division), % (remainder), + (addition), and - (subtraction) operators Those operators are supported by all In the case of integral types, those operators (except the ++ and -- operators) are defined for the int, uint, long, and ulong types. When operands are of other integral types ( sbyte, byte, short, ushort, or char), their values are converted to the int type, which is also the result type of an operation. When operands are of different integral or floating-point types, their values are converted to the closest containing type, if such a type exists. For more information, see the ++ and -- operators are defined for all integral and floating-point numeric types and the Increment operator ++ The unary increment operator ++ increments its operand by 1. The operand must be a variable, a The increment operator is supported in two forms: the postfix increment operator, x++, and the prefix increment operator, ++x. Postfix increment operator The result of x++ is the value of x before the operation, as the following example shows: int i = 3; Console.WriteLine(i); // output: 3 Console.WriteLine(i++); // output: 3 Console.WriteLine(i); // output: 4 Prefix increment operator The result of ++x is the value of x after the operation, as the following example shows: double a = 1.5...

The tutorial shows how to use the MOD function to perform the modulo operation in Excel. You will also learn how finding remainder can help with solving more complex tasks such as summing every Nth cell, highlighting odd or even numbers, and more. The Excel MOD function is designed to get the division remainder. Simple, isn't it? But this function is capable of much more than its original purpose, and in a moment you will learn a few non-trivial uses of MOD in Excel that may prove helpful in your work. • • • • • • • • • • MOD(number, divisor) Where: • Number (required) - the number to be divided. • Divisor (required) - the number to divide by. For example, MOD(10,3) returns 1 because 10 divided by 3 has a quotient of 3 and leaves a remainder of 1 (10=3*3+1). The formula MOD(10,5) returns zero because 10 is divided by 5 without remainder. 3 things you should know about MOD in Excel • The result of the MOD function has the same sign as the divisor. • If the divisor is 0, MOD returns the #DIV/0! error because you cannot divide by zero. • If the number or divisor is a text value, an Excel Mod formula returns the #VALUE! error. MOD formulas to calculate cells In real-life worksheets, the Excel MOD function is rarely used on its own. More often, you will find it as part of bigger formulas that perform various calculations based on division remainder. Mod formula to sum every Nth row or column Surprising at it may seem, Microsoft Excel has no built-in function to sum every 2nd, 3...