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1CP2-P-1.5 Binary foundations checkpoint
Part 5 of 5 · 1CP2-P-1 · Binary foundations
The checkpoint for the whole Binary foundations series, sampling every method the four worksheets taught.
Students will:
- calculate state counts and unsigned maximums correctly
- convert in both directions at the full 8-bit width
- add positive 8-bit integers and identify overflow
- explain what overflow means for a stored reading
- represent and interpret two's complement patterns
Inside: 7 explanation cells, 3 multiple-choice questions, 7 number cells and 1 written answer. 18 marks, about 45 minutes.
Series: 1CP2-P-1 · Binary foundations, part 5 of 5.
Shared by Coding PathwayVerified teacher
- 18 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.
Binary foundations checkpoint
This checkpoint covers only the principles content taught in 1CP2-P-1.1 to 1CP2-P-1.4. It contains no programming-strand questions and introduces no hexadecimal, ASCII, shifts or subtraction.
Each section includes a concise method reminder. Use it to organise your working.
1. Patterns and capacity
Remember: n bits give 2^n unique states. If those states label unsigned values beginning at zero, the maximum is 2^n − 1. The pattern's context supplies its meaning.
Answer one state-count and one unsigned-maximum question.
Read whether each question asks how many values or the largest value.
a)How many different values can 5 bits represent?
b)What is the largest denary number 6 bits can hold?
Why might 01000010 represent a number in one system and a character in another?
- AThe bits are physically rearranged each time.
- BThe current encoding or context supplies the interpretation.
- COnly patterns beginning with 1 have fixed meanings.
- DAll 8-bit patterns are characters.
2. Unsigned conversion
Use headings 128 64 32 16 8 4 2 1.
- Binary to denary: add headings selected by 1 bits.
- Denary to binary: choose largest fitting headings and subtract.
- Keep exactly eight bits and check the unsigned range 0 to 255.
Convert these unsigned 8-bit patterns to denary.
Recall the place values, but complete these without displayed headings.
a)What is 01011001 in denary?
b)What is 10100101 in denary?
Convert these denary values to unsigned 8-bit binary.
Complete these without displayed headings and give exactly eight bits.
a)Convert 58 to 8-bit binary.
b)Convert 198 to 8-bit binary.
3. Addition and overflow
Add from right to left. 1 + 1 = 10, so write 0 and carry 1. A carry used within the method is not automatically overflow. Overflow occurs only when the complete result requires more bits than the assigned location provides.
Add these positive 8-bit binary integers.
Enter both eight-bit totals. Use separate working if needed.
a)Add these 8-bit binary numbers: 00101110 + 00011101.
b)Add these 8-bit binary numbers: 01011011 + 00100111.
Test the width
For an 8-bit unsigned location, first find the full mathematical result and compare it with 0 to 255. If a ninth bit is required, the assigned location cannot represent the complete answer and the program outcome may be incorrect.
Add this pair in an 8-bit unsigned location and decide what happens.
Give the stored 8-bit total and select the reason based on the required width.
Add 11010100 and 01000011 in an 8-bit register, then say what happens to the answer.
A sensor stores an unsigned reading in 8 bits, but a calculation produces denary 300. Explain why this is an overflow and give one likely effect on the system's outcome.
Connect the value to the 8-bit range and the available storage width.
Students type their answer here.
4. Signed and two's complement
Use signed representation when negative values are required. Eight-bit two's complement ranges from −128 to +127 and gives the MSB place value −128.
To construct a negative pattern: write the positive magnitude in eight bits, invert every bit, then add 1. To interpret a negative pattern, use signed place values or recover the magnitude with the same invert-and-add-one operation.
Which data most clearly requires a signed integer representation?
- AThe number of students present.
- BThe number of files stored.
- CA temperature that can fall below zero.
- DThe number of attempts completed.
Write these denary values as 8-bit two's complement patterns.
Choose a reliable method and enter only each final eight-bit pattern.
a)Write −29 as an 8-bit two's complement number.
b)Write −84 as an 8-bit two's complement number.
Interpret this 8-bit two's complement pattern in denary.
Use the signed place values or recover its magnitude.
What is the denary value of the two's complement number 11001101?
Which statement correctly distinguishes 8-bit pattern count from unsigned maximum?
- AThere are 255 patterns and the maximum is 256.
- BThere are 256 patterns and the maximum is 255.
- CThere are 128 patterns and the maximum is 127.
- DBoth answers are 256.
Series checkpoint complete
This evidence covers binary purpose and context, capacity, unsigned conversion, positive addition, overflow and introductory two's complement.
Any insecure area should be retaught from its owning worksheet before the next principles series. 1CP2-P-2 begins by deepening two's-complement conversion, then adds logical and arithmetic shifts, hexadecimal and ASCII.