Carry the one, watch the edge

Computing · Computer Systems · ages 14-15

Name ______________________ Date ____________

You line binary numbers up on the right and add leftward.
Circle one: True False
What is 1 + 1 in binary?
- 10
- 11
- 2
Where does a binary carry go?
- Away, it is dropped
- Left one column
- Back to the right
Does 01101101 + 01011010 still fit in 8 bits?
- Yes: 199 fits in 8 bits
- No, it overflows
- Yes, it equals exactly 256
How many different patterns can 8 bits hold?
Answer: ______________
What does a program show when a value overflows?
- Always a clean zero
- Wraps to a small value
- A longer decimal number
Ana adds 1111 + 1 and writes 1112. What slipped?
- She lined the numbers up left
- She dropped every carry
- Binary has no digit 2, the answer is 10000
What happens when 255 + 1 is stored in 8 bits?
- 256 is stored safely
- 0 with the extra bit lost
- The program always crashes

Answer key

For grown-ups. Fold this page away before handing over the rest.

True · Columns line up on the right so each carry moves left correctly.
10 · Two ones make one two, written 10 with a carry.
Left one column · Each carry joins the next column left, like tens in decimal.
Yes: 199 fits in 8 bits · The sum is 199, and anything up to 255 still fits.
256 · Eight bits give 256 patterns, counting 0 up to 255.
Wraps to a small value · The extra bit falls off, so a small wrapped value or a warning appears.
Binary has no digit 2, the answer is 10000 · Carrying all the way left turns 1111 + 1 into 10000.
0 with the extra bit lost · 256 needs nine bits, so the ninth falls off and 0 stays.