Division by two

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. Similarly, division by any power of two 2k may be performed by right-shifting k positions. Because bit shifts are often much faster operations than division, replacing a division by a shift in this way can be a helpful step in program optimization. An example from Common Lisp: (setq number #b1101001) ; #b1101001 — 105 (ash number -1) ; #b0110100 — 105 >> 1 ⇒ 52 (ash number -4) ; #b0000110 — 105 >> 4 ≡ 105 / 2⁴ ⇒ 6 The above statements, however, are not always true when dealing with dividing signed binary numbers. Shifting right by 1 bit will divide by two, always rounding down. However, in some languages, division of signed binary numbers round towards 0 (which, if the result is negative, means it rounds up). For example, Java is one such language: in Java, -3 / 2 evaluates to -1, whereas -3 >> 1 evaluates to -2. So in this case, the compiler cannot optimize division by two by replacing it by a bit shift, when the dividend could possibly be negative. ==Binary floating point==

In binary floating-point arithmetic, division by two can be performed by decreasing the exponent by one (as long as the result is not a subnormal number). Many programming languages provide functions that can be used to divide a floating point number by a power of two. For example, the Java programming language provides the method java.lang.Math.scalb for scaling by a power of two, and the C programming language provides the function ldexp for the same purpose. ==Decimal==

The following algorithm is for decimal. However, it can be used as a model to construct an algorithm for taking half of any number N in any even base. • Write out N, putting a zero to its left. • Go through the digits of N in overlapping pairs, writing down digits of the result from the following table. Example: 1738/2=? Write 01738. We will now work on finding the result. • 01: even digit followed by 1, write 0. • 17: odd digit followed by 7, write 8. • 73: odd digit followed by 3, write 6. • 38: odd digit followed by 8, write 9. Result: 0869. From the example one can see that 0 is even. If the last digit of N is odd digit one should add 0.5 to the result. ==See also==