Apply bitwise AND, OR, XOR, NOT and shift operations, and use masks to set, clear, toggle and test individual bits

What this dot point is asking

SEAB wants you to apply the bitwise operators AND, OR, XOR and NOT, the left and right shifts, and to use masks to set, clear, toggle and test individual bits. The key idea is that bitwise operators work on each bit position independently, which lets a single byte pack and manipulate many separate flags efficiently.

The answer

The four bitwise operators

Each operator combines two bits position by position (NOT takes one):

• AND (&): 1 only if both bits are 1. Used to clear or isolate bits.
• OR (|): 1 if either bit is 1. Used to set bits.
• XOR (^): 1 only if the bits differ. Used to toggle bits.
• NOT (~): inverts every bit. Used to build the complement of a mask.

  A:   1 1 0 0
  B:   1 0 1 0
A&B:   1 0 0 0
A|B:   1 1 1 0
A^B:   0 1 1 0
 ~A:   0 0 1 1   (within the width)

Shifts

A left shift (<<) moves all bits left, filling with 0 on the right; shifting by $k$ multiplies an unsigned value by $2^k$. A right shift (>>) moves all bits right; for an unsigned value it divides by $2^k$, discarding the remainder.

Masks

A mask is a chosen bit pattern used with an operator to act on specific positions. A single-bit mask for bit $n$ is 1 << n. The standard operations:

mask = 1 << n
value = value | mask        # set bit n to 1
value = value & ~mask       # clear bit n to 0
value = value ^ mask        # toggle bit n
is_set = (value & mask) != 0   # test bit n

Each operation leaves all other bits untouched, which is what makes a single byte a tidy container for up to eight independent flags.

Examples in context

Example 1. Hardware control registers. A device driver configures a peripheral by writing to a control register where each bit enables a feature. Setting bit 4 to turn on an interrupt, without disturbing the other settings, is exactly an OR with 1 << 4 - which is why embedded code is full of masks.

Example 2. File permissions. Unix permissions pack read, write and execute as bits (4, 2, 1). Granting write to an existing permission set is an OR with the write mask, and checking whether a file is executable is an AND with the execute mask tested for non-zero. The chmod number 755 is just three groups of these bit values.

Try this

Q1. Give the Python expression to toggle bit 6 of an integer x. [1 mark]

• Cue. x = x ^ (1 << 6); XOR with the single-bit mask flips that bit.

Q2. Compute $11001100_2$ AND $00111100_2$. [2 marks]

• Cue. Keep bits set in both: $00001100_2$.

Q3. What value results from left-shifting $00000101_2$ by 2, and what arithmetic operation is that? [2 marks]

• Cue. $00010100_2 = 20$; it multiplies $5$ by $2^2 = 4$.