How to Divide Integers With Bit Shifts


Bit shifts offer a method of quickly performing certain mathematical operations, such as multiplication and division, on binary numbers. This type of low-level math significantly speeds execution of programs, since it avoids high-level math operations. Use a bit shift right to divide an integer by a power of two without the need for a calculator or a mathematical mind.

  • Express the dividend (the number that you're dividing) in binary form. The resulting number consists of a series of ones and zeros. Let the number of bits be B.

  • Determine the power of two that represents the divisor. (For example, 4 is 2 to the second power and 16 is 2 to the fourth power.) Let N represent this number.

  • Start a new binary number, writing from left to right, with N zeros. After the zeros, copy the bits from the dividend until the new number has the same number of bits as the dividend. If N is greater than or equal to the number of bits in the dividend, simply write B zeros.

  • Ignore the last N bits of the dividend, since the division (or shift) eliminates these bits. The result is a binary number with the same number of bits as the dividend.

  • Convert the result back to the original form. If the original dividend was in base 10, for example, then convert back to base 10.

Tips & Warnings

  • Integer division using a bit shift only works when the divisor is a power of two, such as 2, 4, 8, 16 and 32.
  • Computers do not convert between base number systems; they operate exclusively in binary. Conversion between base number systems is for the benefit of computer users.
  • The kind of simple division described here involves only integers, so the result is an integer with any remainder discarded.
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