Logical Shifts and Bit Masks

A logical left shift moves every bit left and fills new low-order positions with zero. Bits leaving the fixed-width field are discarded. An eight-bit left shift of 10110100 gives 01101000, unsigned 104. The mathematical product 180×2=360 does not fit eight bits, so this stored result is not the full product.

A logical right shift fills high-order positions with zero. Shifting 10110100 right once gives 01011010, unsigned 90. For unsigned values a right shift divides by two with discarded remainder bits. For a signed negative value, zero-filling changes its sign interpretation; an arithmetic right shift instead repeats the sign bit under the given signed model.

Bitwise AND with a zero mask bit clears that position; a one preserves it. AND 00001111 extracts the low four bits of 10110100, giving 00000100. OR with a one forces that position to one, while a zero preserves it. OR 00000010 sets bit 1, producing 10110110.

XOR with one toggles a bit, while zero leaves it unchanged. XOR 00100000 toggles bit 5, producing 10010100. Number bit positions from zero at the right in these examples. A mask can affect several positions at once. Explain whether the requirement is to test, force, clear or toggle; these actions are not interchangeable.

To test whether a flag is set, AND the word with its mask and compare with zero. Testing a group of flags may require comparing with the whole mask if every selected bit must be one. To clear a selected flag, AND with a width-limited mask that has zero at that position and ones elsewhere.

Python integers are not limited to eight bits, so the example applies & 0xFF after a left shift to model eight-bit storage. It does not claim that every programming language handles shifts or overflow identically. Distinguish a bitwise operation across integer bits from logical AND/OR applied to whole Boolean conditions; similar names do not make their value-level effects identical.

value = 0b10110100
print(format(value & 0b00001111, "08b"))
print(format(value | 0b00000010, "08b"))
print(format(value ^ 0b00100000, "08b"))
print(format((value << 1) & 0xFF, "08b"))
print(format(value >> 1, "08b"))

Attempt the task before opening its worked response. Record each change of state, explain the rule used, and check the result against the original requirements. Code examples labelled Python 3 use that language’s conventions; pseudocode states its own assumptions.