Technologies K–10 · Years 7–8

Eight bits: counting to 255 and overflow

Digital Technologies context (NSW Technology Mandatory 7–8, 2017, outgoing; the Technology 7–8 Syllabus (2023) Digital and communication technologies focus area has no content point on data representation); Digital Technologies: Knowledge and understanding, Data representation (ACARA v9)

Practical, model not builtLow risk

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The idea

Digital systems store integers in a fixed number of binary digits, so an 8-bit value runs from 0 to 255 and a sum that needs a ninth bit wraps around.

What you need

8 binary cards (1 to 128) per pair
Computer with Python 3 (IDLE or Thonny)
Worksheet for column addition in binary

How to do it

Convert 200 and 100 to 8-bit binary with the cards.
Add them in binary by column addition, carrying as in decimal. Note what happens in the ninth column.
Keep only the lowest 8 bits and convert the result back to decimal.
Check in Python: bin(200), bin(100), (200 + 100) & 0xFF and (255 + 1) & 0xFF.
In Python, read the byte 0b10000000 as a signed number with int.from_bytes(bytes([128]), 'big', signed=True), then work out 127 + 1 in signed 8-bit.
Explain why transistors that are either off or on make binary the natural choice for digital systems.

What you should see

200 = 11001000 and 100 = 01100100. Their sum, 300, needs 9 bits; keeping 8 bits gives 00101100, which is 44. 255 + 1 keeps 8 bits of 0, so the value wraps to 0. Read as signed 8-bit (two's complement), 10000000 is −128, so 127 + 1 gives −128. The learner knows it worked when the card sums, the hand column addition and Python agree.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Computers can store any size of number in any variable (fixed-size storage wraps around).
Binary is used because it is faster to write (two states are the most reliable to store and switch).
An overflow always causes an error message (many systems wrap around silently).

Safety card

Low riskLearners carry it out

Hazards

None beyond normal computer use

Controls

Not applicable

Note

No chemicals or heat.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Technology Mandatory 7–8 Syllabus (2017), NESA. Outgoing: replaced by the Technology 7–8 Syllabus (2023) from 2026 and not available after December 2027. Code read from the official syllabus document (DOCX) on 2026-09-22.TE4-7DI
Australian Curriculum v9AC9TDI8K04

Sources

The pages the author read to write this activity.

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