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decomposes a number into significand and a power of 2 ldexp: multiplies a number by 2 raised to a power modf: decomposes a number into integer and fractional parts scalbn scalbln: multiplies a number by FLT_RADIX raised to a power nextafter nexttoward: returns next representable floating-point value towards the given value copysign
0110 (decimal 6) AND 1011 (decimal 11) = 0010 (decimal 2) Because of this property, it becomes easy to check the parity of a binary number by checking the value of the lowest valued bit. Using the example above: 0110 (decimal 6) AND 0001 (decimal 1) = 0000 (decimal 0) Because 6 AND 1 is zero, 6 is divisible by two and therefore even.
It shifts each bit in its left operand to the right. The number following the operator decides the number of places the bits are shifted (i.e. the right operand). Thus by doing ch >> 3 all the bits will be shifted to the right by three places and so on.
This discrepancy has led to bugs in a number of compilers. [8] For example, in the x86 instruction set, the SAR instruction (arithmetic right shift) divides a signed number by a power of two, rounding towards negative infinity. [9] However, the IDIV instruction (signed divide) divides a signed number, rounding towards zero.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.
Logical shifts can be useful as efficient ways to perform multiplication or division of unsigned integers by powers of two. Shifting left by n bits on a signed or unsigned binary number has the effect of multiplying it by 2 n. Shifting right by n bits on an unsigned binary number has the effect of dividing it by 2 n (rounding towards 0).
In binary arithmetic, division by two can be performed by a bit shift operation that shifts the number one place to the right. This is a form of strength reduction optimization. For example, 1101001 in binary (the decimal number 105), shifted one place to the right, is 110100 (the decimal number 52): the lowest order bit, a 1, is removed.