Perform logical left binary shifts
Shift an 8-bit positive binary integer left, track discarded bits and explain the change in value.
Exam scope and assessment notes
This sequence follows Cambridge IGCSE Computer Science 0984, 2026–2028 syllabus Version 4. It covers subject content sections 1.1–1.3 only. The separately published 2029–2031 syllabus is not mapped here. Practice is original, self-checked and does not award an official Cambridge grade. Full timed papers and human subject-teacher review remain outstanding. Cambridge states that 0984 has the same 2026–2028 subject content as 0478, with 9–1 grading. In June and November, Cambridge lists 0984 in Administrative zone 3 and for centres in Oman and the UAE. Confirm availability for your centre and exam series with Cambridge International. The separately published 2029–2031 syllabus changes to Python 3 only and removes pseudocode; this 2026–2028 route does not cover those changes.
Before you begin
- No programming language is required. Be comfortable with place value and multiplication; each lesson introduces the computer-science notation it uses.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which bit enters at the right in a logical left shift?
What you will learn
- Perform a one-place logical left shift
- Perform multiple shifts and identify lost bits
- Relate a left shift to multiplication when no significant bit is lost
Shift without changing the register width
In a logical left shift, every bit moves one place left. A zero enters on the right and the leftmost bit is discarded. Repeat the same rule for each requested shift.
Apply and check the rule
When no significant bit is lost, one left shift multiplies the positive value by two. If a 1 leaves the register, the result no longer equals the original value multiplied by two; the fixed-width pattern has lost information.
Pause and explain
What is the result of shifting 11000000₂ left once in an 8-bit register?
Worked example
Perform a two-place logical left shift on 00101101₂.
Show the worked solution
- After one shift: 01011010; zero enters at the right.
- After a second: 10110100.
- 45×4=180, which fits in eight bits; no 1 was lost.
Answer 10110100₂ (180)
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Shift 00010110₂ left once.
Give me a hint
Move every bit one place toward the most significant end.
Compare my reasoning
- The leftmost bit is 0, so nothing significant is lost.
- Insert 0 at the right.
00101100₂ (44)
Look for these in your work
- Eight-bit width retained
- Result equals 22×2
Shift 00110101₂ left twice.
Give me a hint
Apply the shift twice, checking the leftmost bit each time.
Compare my reasoning
- First shift: 01101010.
- Second shift: 11010100.
- No 1 is discarded; 53×4=212.
11010100₂ (212)
Look for these in your work
- Both shifts shown
- No significant bit lost
- Value check correct
An 8-bit register stores 192 and is shifted left once. Explain why the bit pattern is not a valid representation of 384.
Give me a hint
Inspect the bit shifted out of the register.
Compare my reasoning
- 192 is 11000000₂.
- The leftmost 1 is discarded; zero enters on the right.
- The resulting eight-bit pattern is 10000000₂, which represents 128, not 384.
384 needs nine bits. The fixed-width logical shift drops a leading 1, so the resulting pattern 10000000₂ is 128 and the original information is lost.
Look for these in your work
- 192 converted
- Dropped bit identified
- Result distinguished from arithmetic multiplication
Common mistakes
- Adding zeros on the left instead of shifting every bit
- Ignoring a 1 discarded from the most significant end
What can you explain now?
What is 00001101₂ after a one-place logical left shift?
Compare with the explanation
00011010₂
The bits move left, zero enters on the right, and 13 becomes 26.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
When does a logical left shift stop being equivalent to multiplying by a power of two?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.