Binary shifts

Numbers: Binary shifts

1.2.4a Data Storage: Numbers

Data Storage: Numbers — Note 5 of 5

What you need to know

A binary shift moves all bits in a binary number left or right by a specified number of places. Left shifts multiply the value; right shifts divide it. Bits shifted out are lost, and zeros fill the vacated positions.

What to know

Bits that are shifted beyond the register (past the edge) are LOST.

Key terms

Exam tipCommon mistake

Left Shift: Moves all bits to the left, adding 0s on the right. Equivalent to MULTIPLYING by 2 for each place shifted.
Example: 00101100 (44) left shift by 1 = 01011000 (88). The value has been multiplied by 2.
A left shift of 2 places multiplies by 4 (2x2). A right shift of 3 places divides by 8 (2x2x2).
Exam tip: State the EFFECT on the value — e.g. 'a left shift of 2 multiplies the value by 4'. Do not just describe the movement of bits.
Right Shift: Moves all bits to the right, adding 0s on the left. Equivalent to DIVIDING by 2 for each place shifted.
Exam tip: A right shift of 2 on 11001011 (203) gives 00110010 (50), not 50.75. Binary shifts always round DOWN (lose precision for odd numbers).

Exam technique

Mistake:Forgetting that bits shifted out are lost, which can change the expected result — this causes a loss of PRECISION.

Example:'What shift multiplies by 8?' Answer: left shift of 3 places (2×2×2=8). You need BOTH the direction AND the number of places for full marks.
Example:'Identify the shift applied to 10110000 to get 10000000' — left shift of 3 places. Note the right-most bits that dropped off.

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