Bitwise manipulation and masks: shifts, combining with AND, OR and XOR

Bitwise manipulation and masks: shifts, combining with AND, OR, and XOR

1.4.1 Data Types

Data Types — Note 9 of 10

Candidates should be able to perform right and left logical shifts. Candidates should understand the effect of right and left shifts on a binary numbers. Candidates should understand the purpose of using masks with bitwise operators, and should have experience of applying masks using AND, OR and XOR.

What you need to know

Bitwise operations work on the individual bits of a binary value. Shifts move bits left or right, and masks combined with AND, OR or XOR can check, clear, set or toggle particular bits.

What to know

A left shift of n places multiplies an unsigned value by 2^n; a right shift of n places divides by 2^n (rounding down).
Uses: extracting part of a value (e.g. the lower nibble), setting or clearing status flags, checking whether a number is odd (AND with 00000001).

Key terms

Exam tipCommon mistake

Logical shift: All bits move left or right by a number of places; bits shifted out are lost and the empty positions are filled with 0s.
Mask: A binary pattern combined with a value using a bitwise operator to select or change particular bits.
AND with a mask: CLEARS bits where the mask is 0 and KEEPS bits where the mask is 1. Used to check or extract bits.
OR with a mask: SETS bits to 1 where the mask is 1, and leaves the others unchanged.
XOR with a mask: TOGGLES (flips) bits where the mask is 1, and leaves the others unchanged.
Exam tip: Write the value and mask directly above each other and work through column by column.

Exam technique

Mistake:Forgetting that bits shifted off the end are lost, which can change the result unexpectedly.

Code examples

Masks with AND, OR and XOR

text

Value       1 0 1 1 0 1 1 0
AND mask    0 0 0 0 1 1 1 1   -> 0 0 0 0 0 1 1 0  (keep lower nibble)
OR  mask    1 0 0 0 0 0 0 0   -> 1 0 1 1 0 1 1 0  (set the MSB)
XOR mask    1 1 1 1 1 1 1 1   -> 0 1 0 0 1 0 0 1  (flip every bit)

Shift left 1:   0 1 1 0 1 1 0 0  (MSB lost)
Shift right 2:  0 0 1 0 1 1 0 1