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.
Binary Shifts - Fast Multiplication and Division
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)
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.