The present invention is a variable-delay division (VDD) scheme implementable in hardware to execute signed and unsigned integer division and remainder operations in digital processor. The VDD scheme advantageously uses hardware utilized for multiplication to implement a 2-bits/cycle alignment step to iteratively align the divisor with the dividend. This speeds up the alignment phase of integer division. Quotient bits are produced at the rate of 1-bit/cycle using the well-known restoring scheme. For 32-bit 2's complement operands, the scheme has a delay less than a fixed-delay scheme for most operands.