Loss of Accuracy and Overflow in Shifts

A binary pattern has a fixed width, such as 8 bits. When a shift moves a bit past either end, that bit is gone: it is not wrapped round to the other end. This matters because the value you keep can be smaller or less exact than the true result.

Right shifts lose accuracy

A right shift divides by a power of two, but the bits that fall off the right-hand end are discarded. For a positive number this means the result is rounded down. For example, the 8-bit unsigned pattern 00110101 (53) shifted right by one place becomes 00011010 (26). The final 1 is discarded, so 53 ÷ 2 = 26.5 becomes 26.

For an arithmetic right shift of a negative two's complement number, the effect is to round towards negative infinity. The 8-bit pattern 11111001 represents -7. Shifted right by one place it becomes 11111100, which is -4. The true answer -3.5 has been rounded down, not towards zero.

Left shifts can overflow

A left shift multiplies by a power of two, but any 1 bits pushed beyond the most significant bit are lost. If this changes the value, the shift has caused overflow. For example, the 8-bit unsigned pattern 10011100 (156) shifted left by one place becomes 00111000 (56). The leading 1 has been shifted out of the fixed-width pattern, so the result is not 312.

The result of any shift therefore depends on its direction, how many places it moves and the fixed width of the pattern.