Convert Any Radix Base Number to Decimal or to Any Other Radix Base Number. Type the number in the box and then click "Click to Convert" You may type the decimal point. When you convert a Decimal number to another base, the Decimal Fraction (the number to the right of the decimal point) will convert to a Fraction in the other base. When you convert a number from another base to a Decimal number, the fraction in the other base will be ignored. If you type "101111.011", the computer will use "101111" to calculate the answer. To Convert a Binary Fraction to a Decimal Fraction, enter the Binary Fraction to the right of the decimal point. For example, if the number is "101111.011", type "011" to the right of the decimal point. To clear the entry boxes click "Reset". Decimal (base 10) 983,232 converts to F00C0 Hexadecimal (base 16). JavaScript Error If you try to convert .7 Decimal to Binary, the result is: 0.1011001100110011001100110011001100110011001100110011... .5 in Decimal will convert to 0.1 Binary exactly.
The Euclidean Algorithm. The task for today is to find the fastest algorithm to calculate the greatest common divisor (GCD) of a pair of numbers. The GCD has a number of properties that allow us to express the GCD of a pair of larger numbers as the GCD of smaller numbers. By using recursion, this leads to a solution. The first of the above identities follows from convention, where zero divides zero zero times (instead of one time). This makes some identities with the least-common-multiple simpler. So how should we benchmark an algorithm for this problem? The difficulty is that the GCD of of a pair of two numbers can be quite different to the GCD of another pair, even if the two pairs are quite close in magnitude. To solve these problems, we allocate a large array to hold 224 pairs of random numbers. Euclidean Algorithm Since the algorithm above is tail-recursive, we can re-express it in an iterative form: typedef unsigned long long u64b; u64b gcd0(u64b u, u64b v) { /* Special case when input is zero */ if (!
Extension of Euclid's Algorithm. We already know that, for any two whole numbers a and b, there exist integers s and t such that In other words, gcd(a,b) is a linear combination of a and b. gcd(a,b) is the Write the two linear combinations in a column and apply one step of Euclid's algorithm to the left-hand side. Assuming Multiply the second equation by p and subtract it from the first equation: a = 1·a + 0·b b = 0·a + 1·b r = 1·a + (-p)·b Apply the same procedure to the last two equations.
Therefore, 20·2322 - 71·654 = 6. The algorithm, as described above, is a real extension of Euclid's algorithm in the sense that without removing any of the operations needed for the latter it only adds 2 multiplications and 2 subtractions on every step. Indeed, assume the extended algorithm has furnished s,t, and g such that as + bt = g. On Internet Applet for Euclid's Algorithm (Extended) |Contact||Front page||Contents||Algebra||Store| The Euclidean Algorithm. Stein's Algorithm. Greatest Common Divisor In an earlier article I showed a C# version of the Euclidean algorithm, described by the Greek mathematician, Euclid of Alexandria.
This algorithm can be used to calculate the greatest common divisor (GCD) of two integers. The GCD is the largest whole number that both integers can be divided by without generating a remainder. For example, the GCD of 210 and 124 is 42, as both values can be divided by 42 without remainder, giving results of 5 and 3 respectively. The most basic version of the Euclidean algorithm works by repeated subtraction. I won't describe it here as it is covered in the earlier article. NB: The method is shown as static so that it can be called directly from the Main method of a console application project. Stein's Algorithm Stein's algorithm, published in 1967 by Josef Stein, is another algorithm for calculating the GCD of two values. Stein's algorithm uses a number of rules: Creating the Stein Method Testing the Method. C# - Convert int to a bit array in .NET. Shift Operators. Shift moves bit positions. It changes the bit representation of a type.
The bits are shifted right (or left) a number of positions. The C# language enables bitwise shifting by offering the right shift (>>) and left shift (<<) operators. Example We introduce a program that shows the right shift (>>) and then left shift (<<) bitwise operators in the C# language. We repeatedly apply them and change the value of a random integer of an int type. Note:The output of the program illustrates how the bit values are changed with the parameters to the shift operators. Note 2:The output also shows the decimal value of the integer is influenced by these shifts. This program introduces the Program class. Random Next, the program uses a loop. And:The following loop repeats this, but pushes the bits to the left by using the left shift (<<) operator.
Note:The left shift changes the decimal value of the output because the sign bit is changed by this operation. Uses GetHashCodeDivide by Powers of Two Summary. C# - Identify odd, even numbers - binary vs. mod. Binary GCD algorithm. The binary GCD algorithm, also known as Stein's algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm was first published by the Israeli physicist and programmer Josef Stein in 1967,[1] it may have been known in 1st-century China.[2] Algorithm[edit] The algorithm reduces the problem of finding the GCD by repeatedly applying these identities: gcd(0, v) = v, because everything divides zero, and v is the largest number that divides v.
Similarly, gcd(u, 0) = u. gcd(0, 0) is not typically defined, but it is convenient to set gcd(0, 0) = 0.If u and v are both even, then gcd(u, v) = 2·gcd(u/2, v/2), because 2 is a common divisor.If u is even and v is odd, then gcd(u, v) = gcd(u/2, v), because 2 is not a common divisor. Implementation[edit] Efficiency[edit] Binary Euclid's Algorithm.
Euclid's algorithm is tersely expressed by the recursive formula where (N mod M) is the remainder of division of N by M. We postulate gcd(N,0) = N in accordance with the end condition of Euclid's algorithm. Our example appears as gcd(2322,654) = gcd(654,360) = gcd(360,294) = gcd(294,66) = gcd(66,30) = gcd(30,6) = gcd(6,0) = 6. Other properties of gcd are expressed in such a similarly concise form gcd(KN, KM) = K gcd(N, M) If gcd(N,M) = 1 then gcd(N,MK) = gcd(N,K) gcd(N, M) = gcd(N - M, M) There are many ways to prove these. If N and M are even, gcd(N, M) = 2 gcd(N/2, M/2), If N is even while M is odd, then gcd(N, M) = gcd(N/2, M), If both N and M are odd, then (since N-M is even) |N-M| < max(N,M). The algorithm is known as binary because, unlike the original one, it does not use general division of integers but only division by 2.
Another handy operation is a bitwise conjunction &. The Using our example: The algorithm is a slight improvement over the original method.