Students will be expected to understand and use only a logical binary shift.

The idea

A logical binary shift moves every bit in a binary pattern a stated number of places left or right and fills the vacated positions with 0. A left shift by n places multiplies the value by 2ⁿ; a right shift by n places divides by 2ⁿ, discarding bits shifted off the right-hand end. For example, 0000 1011 (11) shifted left by 2 gives 0010 1100 (44), and 0000 1011 shifted right by 2 gives 0000 0010 (2), because the two lowest bits are lost. The specification limits you to logical shifts only, so you are not required to handle arithmetic shifts that preserve a sign bit. Track the bit pattern and the place value together, and state the number of places moved.

What earns the marks

• A logical shift fills vacated bit positions with 0, not with a copied sign bit.
• A left shift by n places multiplies the binary value by 2ⁿ.
• A right shift by n places divides by 2ⁿ, discarding bits shifted beyond the right-hand end.
• The number of places shifted must be identified and applied to every bit in the pattern.
• Only logical shifts are required; arithmetic shifts that preserve a sign bit are outside the expected scope.

Common mistakes and how to put them right

• Filling vacated positions with a 1 or a copied sign bit.

  Put it right by filling every vacated position with 0 for a logical shift.

• Shifting the wrong direction for multiplication.

  Put it right by remembering a left shift multiplies and a right shift divides.

• Forgetting that right-shifted bits are lost.

  Put it right by discarding bits moved past the right-hand end rather than wrapping them round.

Exam tips

• Write the original bit pattern and the shifted pattern side by side so each bit's movement is visible.
• State the number of places shifted and whether it is left or right before calculating the new value.
• Check your answer by converting both patterns to denary and confirming the multiply-or-divide relationship.