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J277 1.2.4 Binary shifts and consolidation
Part 5 of 5 · J277 1.2.4 · Number systems
Binary shifts, then a mixed checkpoint over the whole OCR number-systems topic.
Students will:
- carry out left and right binary shifts
- connect the number of places with a power of two
- identify direction and places from a before-and-after pair
- explain when a fixed-width shift loses information
- apply conversion, addition and overflow independently
Inside: 5 text sections, 3 multiple-choice activities, 2 written answers, 6 number activities. 28 marks. Suggested teaching time: 40–60 minutes. 1 diagram.
Includes a teacher guide with suggested sections, timings and common misconceptions.
Series: J277 1.2.4 · Number systems, part 5 of 5.
Shared by Coding PathwayVerified teacher
- 16 cells
- About 45 minutes
- CC BY-SA 4.0
- Shared 17 Aug 2026
- Updated 27 Oct 2026
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The whole resource, exactly as a class sees it. Answers and marking are held back.
Binary shifts and consolidation
A shift moves every bit left or right. Practise the movement, connect it to multiplication or division, then use the number-system methods together.
1. Move every bit
- A left shift moves bits left and fills empty positions at the right with zeros. Moving n places multiplies by 2^n when the result fits.
- A right shift moves bits right and fills empty positions at the left with zeros. Moving n places gives whole-number division by 2^n; a remainder is lost.
One place uses 2, two places use 4, and three places use 8. These are logical shifts of the non-negative values used here.
For an odd value, a right shift can lose a remainder: 00001101 (13) right by 1 becomes 00000110 (6).
Which statement correctly describes the effects when no significant bit is lost?
- ALeft by 3 multiplies by 3
- BLeft by 2 divides by 4
- CLeft by 2 multiplies by 4; right by 3 divides by 8
- DLeft by 8 multiplies by 8
Shift each value left by two places, then give its denary value.
a)Apply a logical shift left of 2 places to 00010011.
b)Apply a logical shift left of 2 places to 00110001.
Shift each value right by three places, then give its denary value.
a)Apply a logical shift right of 3 places to 10010000.
b)Apply a logical shift right of 3 places to 00101101.
2. A bit can leave the row
The row stays eight bits wide. A bit beyond either edge is discarded.
For example, 11110000 left by 1 becomes 11100000: the leftmost 1 is lost. The stored result is therefore not the full value of 240 × 2. A right shift can similarly discard 1 bits that represent a remainder.
What is the eight-bit result of shifting 11000000 left by one place?
- A01100000
- B110000000
- C11000001
- D10000000
Identify the direction and number of places in each shift.
a)00010101 became 10101000. Which shift was applied, and by how many places?
b)10110100 became 00101101. Which shift was applied, and by how many places?
A program must multiply an eight-bit value by 8. The complete result fits. Describe the binary shift needed.
Students type their answer here.
3. Bring the methods together
Complete the next tasks independently. Give eight-bit binary and two-digit hexadecimal answers where requested. Use the addition carry row to show the binary column method.
Complete each row's two missing representations.
a)Binary 10110110. Fill in the denary and hexadecimal.
b)Hexadecimal 2F. Fill in the denary and binary.
Add each eight-bit pair and show every carry.
a)Add these 8-bit binary numbers: 01100101 + 00111011.
b)Add these 8-bit binary numbers: 00110111 + 01001101.
Add the values and enter only the eight stored result bits.
Add these 8-bit binary numbers: 11001000 + 01100100.
An eight-bit register adds 11001000 and 01100100. Why does this addition overflow?
- AThe complete sum is 300, above the eight-bit maximum 255
- BEvery carry within a binary addition proves overflow
- CAny answer containing a zero has overflowed
- DTwo eight-bit numbers can never be added without overflow
An eight-bit register shifts 11000000 left by one place and stores 10000000. Explain why its stored value is not the exact doubled value.
Students type their answer here.
Review
Choose one response to improve. Check the conversion width, every carry, or both parts of a shift description before retrying it.