Bit manipulation — common mistakes

Examiners frequently test the difference between Logical and Arithmetic shifts. Always check if the question specifies a signed (two's complement) or unsigned number. If signed, use ASR for right shifts. If unsigned, use LSR. If the question doesn't specify, state your assumption, but LSR is the default for 'logical shift'.

Bitwise operations like shifting and logical AND/OR/XOR often map directly to single, extremely fast instructions on the CPU. A multiplication like x * 4 might involve several steps, whereas a bit shift $x << 2$ is a single CPU cycle on most architectures, making it significantly more efficient.

It's mainly for conceptual consistency and completeness in instruction set design. While the result is identical (vacant LSB is filled with 0), having an ASL instruction allows a programmer or compiler to signify that they are performing a multiplication on a signed number, even if the underlying mechanism is the same as for an unsigned one. For your exams, you must know they are functionally identical.

By convention, bit 0 is the rightmost bit (the least significant bit, LSB). Bit 1 is the next one to the left, and so on. For an 8-bit byte, the bits are numbered 7, 6, 5, 4, 3, 2, 1, 0 from left to right. If an exam question deviates from this, it will be explicitly stated.

Not directly with a simple shift. Bit shifts only work for multiplication and division by powers of 2 (2, 4, 8, 16...). Dividing by other numbers requires more complex algorithms, though some can be optimised using a combination of shifts, additions, and subtractions.