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1CP2-P-2.4 Binary shift applications and limitations

Part 4 of 7 · 1CP2-P-2 · Signed data and encoding

The applications worksheet, giving students a five-step method for choosing and defending a shift.

Students will:

  • follow a five-step method from requirement to justified answer
  • identify the direction and number of places from a pair of patterns
  • apply a shift to an unsigned value and state the stored result
  • choose a shift that divides a signed value while preserving its meaning
  • state the question that must be answered before choosing a shift type

Inside: 7 explanation cells, 2 multiple-choice questions, 1 number cell, 1 fill-in-the-blanks cell and 3 written answers. 20 marks, about 45 minutes.

Series: 1CP2-P-2 · Signed data and encoding, part 4 of 7.

Shared by Coding PathwayVerified teacher

  • 14 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 17 Aug 2026

Preview

The whole resource, exactly as a class sees it. Answers and marking are held back.

Binary shift applications and limitations

This consolidation worksheet asks you to select a shift, apply it and explain its effect. Always identify whether the data is unsigned or two's-complement signed before choosing the fill rule.

1. A five-step method

  1. Label the representation and width.
  2. Translate the power of two into shift places.
  3. Choose logical or arithmetic and the direction.
  4. Move bits and apply the correct fill rule.
  5. Interpret the result and check for discarded information or overflow.
Fill in the blanks4 marks
Unsigned ×8 uses a logical shift gap 1 by gap 2 places. Signed ÷4 uses an arithmetic shift gap 3 by gap 4 places.
  • 2
  • 3
  • left
  • right
Number systems4 marks

Identify each shift's direction and number of places.

Use the before and after patterns; do not infer the representation yet.

a)00011010 became 01101000. Which shift was applied, and by how many places?

Before
00011010
After
01101000
DirectionNot answered
PlacesNot answered

b)11110000 became 00011110. Which shift was applied, and by how many places?

Before
11110000
After
00011110
DirectionNot answered
PlacesNot answered

2. Unsigned application

An unsigned value 00110100 is 52. Logical right shift by one gives 00011010, which is 26. No 1 is discarded at the right, so division by two is exact.

Written answer4 marks

Unsigned 01100101 is shifted logically right by two. Give the resulting pattern, the stored denary value and explain any loss of precision.

Compare integer division with the exact quotient.

Students type their answer here.

3. Signed application

Arithmetic right shift is appropriate for dividing a signed two's-complement value by a power of two because it copies the sign bit. Logical right shift would reinterpret many negative inputs as positive.

Written answer4 marks

Choose and apply a shift that divides 11100100 (−28) by 4 while preserving signed meaning. State the type, direction, places, pattern and denary result.

Four is 2 squared. Preserve the leading sign.

Students type their answer here.

4. Do not overstate the shortcut

For unsigned values, a logical left shift can multiply by a power of two only when the intended result fits the stated width. Do not treat arithmetic left shift as a reliable multiplication method for negative values because the original sign bit is moved and may be discarded.

Right shifts may also lose precision: discarded low-order 1 bits represent remainder information that an integer result cannot store.

Multiple choice1 mark

Which is the strongest explanation of a right-shift precision loss?

  • AThe pattern became shorter.
  • BA zero appeared in the pattern.
  • CDiscarded rightmost 1 bits contained remainder information that the integer result cannot store.
  • DEvery shift creates overflow.

5. Mixed decision

A system stores signed temperatures in 8-bit two's complement. A programmer proposes a logical right shift to halve every reading. Evaluate the proposal.

Written answer2 marks

Evaluate using one positive and one negative example, then recommend the correct operation.

A conclusion needs evidence from both signs.

Students type their answer here.

Multiple choice1 mark

Which question must be answered before choosing between logical and arithmetic right shift?

  • AHow many characters are stored?
  • BIs the pattern interpreted as unsigned or signed two's complement?
  • CWas hexadecimal used previously?
  • DDoes the number have eight set bits?

Route forward

You can now select and justify shifts rather than treating them as mechanical movement. Next, hexadecimal provides a compact human-readable shorthand for binary.