Left Shift: Multiply by 2
Shifting all bits one position to the left multiplies the number by 2. Fill the rightmost bit with 0.
Original: 00000101 (5) Left shift 1: 00001010 (10) ← Multiplied by 2 Left shift 2: 00010100 (20) ← Multiplied by 4 Left shift 3: 00101000 (40) ← Multiplied by 8 Why? Each position is worth 2× the previous position!
Right Shift: Divide by 2
Shifting all bits one position to the right divides the number by 2 (integer division - drops remainder). Fill the leftmost bit with 0.
Original: 00101000 (40) Right shift 1: 00010100 (20) ← Divided by 2 Right shift 2: 00001010 (10) ← Divided by 4 Right shift 3: 00000101 (5) ← Divided by 8
What Happens to Odd Numbers?
Original: 00000111 (7)
Right shift 1: 00000011 (3) ← 7÷2 = 3.5, but we get 3 (integer division)
↑
The LSB (1) is lost - remainder is dropped!
Why Shifts are Fast:
- Shifting is a single CPU cycle (very fast)
- Multiplication/division by powers of 2 is instant
- Graphics engines use shifts extensively for scaling
- Example: To multiply by 16, shift left 4 times (2⁴ = 16)
This key facts covers Binary Shifts - Fast Multiplication and Division within Binary Arithmetic for GCSE Computer Science. Revise Binary Arithmetic in 3.3 Data Representation for GCSE Computer Science with 15 exam-style questions and 18 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 11 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Binary Arithmetic
In binary addition, what is the result of 1 + 1?
Explain the effect of a logical left shift and a logical right shift on the value of a binary number.