Sigma Learn

1aEasy1 mark

Which statement most accurately matches the lesson evidence for “Why computers use binary: bits, bytes and magnitude”?

2aEasy1 mark

Which statement most accurately matches the lesson evidence for “The three number systems and place value”?

3aEasy1 mark

Which statement most accurately matches the lesson evidence for “Converting denary and hexadecimal”?

4aEasy1 mark

Which statement most accurately matches the lesson evidence for “Binary addition, subtraction and multiplication at fixed width”?

5aEasy1 mark

Which statement most accurately matches the lesson evidence for “Binary addition, subtraction and multiplication at fixed width”?

6aEasy1 mark

Which statement most accurately matches the lesson evidence for “Signed overflow and range failure”?

7aEasy5.000000001 marks

Classify the source statements from Number Bases, Binary Arithmetic and Overflow by the role they play in a defensible answer.

Core idea or definition

Method, procedure or mechanism

Application, condition or consequence

8aEasy5.000000001 marks

Independently classify this second set of lesson evidence. For each, decide whether it supplies a core idea, a mechanism, or an application/condition rather than relying on a single keyword.

Core idea or definition

Method, procedure or mechanism

Application, condition or consequence

9aEasy2 marks

Put the authentic stages from “Converting 156 to 8-bit binary” in order. Keep the mechanism connected to the lesson evidence rather than arranging terms alphabetically.

1.
AUse 128 — 128 fits into 156. Write 1; $r e main d er = 28$ .
2.
BCheck 64 — 64 does not fit into 28. Write 0; remainder stays 28.
3.
CCheck 32 — 32 does not fit into 28. Write 0; remainder stays 28.
4.
DUse 16 — 16 fits into 28. Write 1; $r e main d er = 12$ .
5.
EUse both — 12 − 8 = 4, then 4 − 4 = 0. Write 1 and 1.

10aEasy3 marks

Use the lesson's wording to explain “Why computers use binary: bits, bytes and magnitude” in two or three precise sentences. Include one implication from:

unsigned range for n bits = 0 to 2^{n} - 1

Your evidence-based response

0 / 200 words

11aMedium4 marks

Use the source comparison “Units of information”. Complete the missing Meaning entries without replacing the lesson's stated distinction.

Unit or prefix	Meaning
bit	Meaning
byte	Meaning

12aMedium2 marks

After ordering the stages, identify the first step that would make a later conclusion unreliable if it were skipped. Put the authentic stages from “Converting 156 to 8-bit binary” in order. Keep the mechanism connected to the lesson evidence rather than arranging terms alphabetically.

1.
ACheck 32 — 32 does not fit into 28. Write 0; remainder stays 28.
2.
BUse 16 — 16 fits into 28. Write 1; $r e main d er = 12$ .
3.
CUse both — 12 − 8 = 4, then 4 − 4 = 0. Write 1 and 1.
4.
DUse 128 — 128 fits into 156. Write 1; $r e main d er = 28$ .
5.
ECheck 64 — 64 does not fit into 28. Write 0; remainder stays 28.

13aMedium4 marks

Work through this lesson-owned case: Explain or demonstrate: Multiply unsigned binary integers using the shift-and-add method and state the width the exact product needs.

Your evidence-based response

0 / 200 words

14aMedium4 marks

Work through this second lesson-owned case: For 101101₂, the 1 bits contribute 32, 8, 4 and 1. The zero bits contribute nothing.

Your evidence-based response

0 / 200 words

15aMedium4 marks

A student applies the conclusion from case A to case B without checking this condition: “

10110 1_{2} = 1 \times 2^{5} + 0 \times 2^{4} + 1 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 4 5_{10}

Writing a base subscript is useful when a question contains several representations.”. Explain why that move may fail, then repair the reasoning for case B.

Your evidence-based response

0 / 200 words

16aMedium5 marks

Explain case A (Explain or demonstrate: Multiply unsigned binary integers using the shift-and-add method and state the width the exact product needs.). Use this condition to assess the explanation: “

10110 1_{2} = 1 \times 2^{5} + 0 \times 2^{4} + 1 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 4 5_{10}

Writing a base subscript is useful when a question contains several representations.”. Write your response, including the one piece of evidence that made you revise or confirm it.

Your evidence-based response

0 / 200 words

17aMedium5 marks

Compare cases A and B. Identify one shared lesson idea and one difference in evidence, method, assumption or outcome. A: Explain or demonstrate: Multiply unsigned binary integers using the shift-and-add method and state the width the exact product needs. B: For 101101₂, the 1 bits contribute 32, 8, 4 and 1. The zero bits contribute nothing.

Your evidence-based response

0 / 200 words

18aMedium4 marks

Use “Converting 156 to 8-bit binary” to explain why the sequence changes the answer or outcome in this case: A sensor sends the unsigned binary value 10101101. (a) Convert it to denary. (b) Convert it to hexadecimal. (c) Encode the denary value 45 in BCD. (d) A file is labelled 2 KiB. How many bytes and how many bits is this?

Your evidence-based response

0 / 200 words

19aMedium1 mark

For case C — A sensor sends the unsigned binary value 10101101. (a) Convert it to denary. (b) Convert it to hexadecimal. (c) Encode the denary value 45 in BCD. (d) A file is labelled 2 KiB. How many bytes and how many bits is this? — which evidence check is most defensible before accepting a conclusion?

20aMedium4 marks

A response quotes “

0011011 0_{2} + 0000110 1_{2} = 0100001 1_{2}

” but never connects it to case C. Diagnose the missing reasoning step and replace it with a supported conclusion.

Your evidence-based response

0 / 200 words

21aMedium5 marks

Independently solve or explain a new instance built from “Binary addition, subtraction and multiplication at fixed width”. State the relevant variable, representation, rule or causal mechanism; then give one condition that could change the conclusion.

Your evidence-based response

0 / 200 words

22aHard5 marks

Change one stated input, assumption, unit, data value, incentive or system constraint in case A: Explain or demonstrate: Multiply unsigned binary integers using the shift-and-add method and state the width the exact product needs. Decide whether the original source conclusion still follows and justify your decision with lesson evidence.

Your evidence-based response

0 / 200 words

23aHard6 marks

Evaluate this lesson claim in the context of case B: “

0111111 1_{2} + 0000000 1_{2} = 1000000 0_{2}

” Give one reason it applies, one limitation or counter-condition, and a final judgement.

Your evidence-based response

0 / 200 words

24aHard6 marks

Create a concise evidence chain connecting “The three number systems and place value”, “Converting denary and hexadecimal”, and case C. Explain how each link supports or limits the final outcome.

Your evidence-based response

0 / 200 words

25aHard5 marks

Create an annotated flowchart, trace table, data layout, state diagram, packet path, or component diagram for case A: Explain or demonstrate: Multiply unsigned binary integers using the shift-and-add method and state the width the exact product needs. Make the mechanism and condition “

10110 1_{2} = 1 \times 2^{5} + 0 \times 2^{4} + 1 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 4 5_{10}

Writing a base subscript is useful when a question contains several representations.” visible.

Draw with the mouse or a finger.

26aHard5 marks

Create an annotated flowchart, trace table, data layout, state diagram, packet path, or component diagram for case B: For 101101₂, the 1 bits contribute 32, 8, 4 and 1. The zero bits contribute nothing. Use labels to show how the evidence leads to your conclusion.

Draw with the mouse or a finger.

27aHard5 marks

Create an annotated flowchart, trace table, data layout, state diagram, packet path, or component diagram for case C: A sensor sends the unsigned binary value 10101101. (a) Convert it to denary. (b) Convert it to hexadecimal. (c) Encode the denary value 45 in BCD. (d) A file is labelled 2 KiB. How many bytes and how many bits is this? Include a labelled limitation, assumption or boundary that would affect the outcome.

Draw with the mouse or a finger.

28aHard5.000000001 marks

Examiner audit: sort each Number Bases, Binary Arithmetic and Overflow claim by its role in a high-quality response. Then use the placement to explain how you would avoid unsupported recall in a long answer.

Core idea or definition

Method, procedure or mechanism

Application, condition or consequence

29aHard6 marks

Choose the more convincing of cases A and B as evidence for “Why computers use binary: bits, bytes and magnitude”. Justify the decision by comparing the specific conclusions and the condition “

10110 1_{2} = 1 \times 2^{5} + 0 \times 2^{4} + 1 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 4 5_{10}

Writing a base subscript is useful when a question contains several representations.”.

Your evidence-based response

0 / 200 words

30aHard7 marks

Create one fully specified new Computer Science case that combines the evidence in “Why computers use binary: bits, bytes and magnitude”, “The three number systems and place value”, and “Converting denary and hexadecimal”. Solve, trace, diagram or analyse it as appropriate; state the condition “

10110 1_{2} = 1 \times 2^{5} + 0 \times 2^{4} + 1 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 4 5_{10}

Writing a base subscript is useful when a question contains several representations.”; and finish with a justified conclusion.

Your evidence-based response

0 / 200 words

Number Bases, Binary Arithmetic and Overflow Assessment

Questions