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1CP2-P-2.3 Arithmetic binary shifts
Part 3 of 7 · 1CP2-P-2 · Signed data and encoding
The arithmetic shift worksheet, and the reason a signed value needs a different operation from an unsigned one.
Students will:
- apply an arithmetic right shift that preserves the sign bit
- compare logical and arithmetic right shifts on the same pattern
- state the defining difference between the two
- explain why arithmetic left shift is not a safe way to double a negative
- justify the result of a shift in denary terms
Inside: 6 explanation cells, 2 multiple-choice questions, 3 number cells, 1 fill-in-the-blanks cell and 2 written answers. 18 marks, about 45 minutes.
Series: 1CP2-P-2 · Signed data and encoding, part 3 of 7.
Shared by Coding PathwayVerified teacher
- 14 cells
- About 45 minutes
- CC BY-SA 4.0
- Shared 17 Aug 2026
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The whole resource, exactly as a class sees it. Answers and marking are held back.
Arithmetic binary shifts
Arithmetic shifts are used with signed two's-complement values. An arithmetic right shift copies the original sign bit into vacated left positions so that a negative value remains negative. Arithmetic left shift inserts zeroes at the right, like logical left shift, but must be interpreted within the signed range.
1. Preserve the sign on a right shift
11101000 is −24. Arithmetic right shift by two:
11101000 → 11111010
Two copies of the original sign bit 1 enter from the left. 11111010 is −6, so the operation divides −24 by 4. A logical right shift would insert zeroes and incorrectly turn the pattern positive.
- 0
- 1
- discarded bit
- sign bit
Apply an arithmetic right shift by two places to these signed 8-bit patterns.
Copy the original sign bit into both vacated positions.
a)Apply a arithmetic shift right of 2 places to 11101000.
b)Apply a arithmetic shift right of 2 places to 10110000.
Compare the results of logical and arithmetic right shift by one on 11100000. Explain which result preserves the signed meaning.
State both patterns and discuss their new leading bit.
Students type their answer here.
2. Positive arithmetic right shifts
For a positive two's-complement value, the sign bit is 0, so arithmetic and logical right shifts produce the same bit pattern. The reason is still different: arithmetic shift copies the sign bit; it just happens to be zero.
Apply an arithmetic right shift by one place.
The patterns are positive, so copy their zero sign bit.
a)Apply a arithmetic shift right of 1 place to 00111000.
b)Apply a arithmetic shift right of 1 place to 01010110.
3. Arithmetic left shift: a crucial limitation
An arithmetic left shift moves every bit left and inserts zero on the right; it does not copy and preserve the original sign bit. For a positive value whose doubled result fits, 00010101 (+21) becomes 00101010 (+42).
Do not use arithmetic left shift as a general method for multiplying negative values. The most significant sign bit moves left and can be discarded, so the stored pattern can have the wrong sign or overflow the 8-bit range. Pearson specifically expects this limitation.
Apply an arithmetic left shift by one place to each positive signed pattern.
Interpret each result as 8-bit two's complement and confirm that the intended doubled value fits.
a)Apply a arithmetic shift left of 1 place to 00010101.
b)Apply a arithmetic shift left of 1 place to 00100100.
Why must 10110000 (−80) not be arithmetically shifted left as a method of multiplying it by two?
- AA zero is inserted on the right, so the pattern becomes unsigned automatically.
- BThe sign bit is shifted out and −160 cannot fit in the 8-bit signed range, producing a misleading positive pattern.
- CArithmetic shifts can only move unsigned values.
- DThe value must first be written in hexadecimal.
4. Apply and justify
When explaining an arithmetic shift, include the representation, direction, places, fill rule, resulting pattern and interpreted signed value.
The 8-bit two's-complement value 11011000 represents −40. Apply an arithmetic right shift by two and explain the denary effect.
Copy the sign bit twice, then interpret the result.
Students type their answer here.
What is the defining difference between logical and arithmetic right shifts?
- AArithmetic right shift copies the sign bit; logical right shift inserts zeroes.
- BLogical right shift copies the sign bit; arithmetic inserts ones.
- CArithmetic right shift always moves two places.
- DLogical right shift works only on negative values.
Route forward
You can now apply arithmetic shifts and distinguish them from logical shifts. The next worksheet consolidates shift selection, effects and information loss in exam-style contexts.