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 fit in 8 unsigned bits?
- No. The 8-bit result has a ninth carry.
- Yes. The sum is 11000111, which is 199.
- Yes. The sum is 11111111, which is 255.
How many different patterns can 8 bits hold?
Answer: ______________
An unsigned 8-bit sum needs a ninth bit. Which choice describes what a program may do?
- Fit all nine bits into the same 8-bit space unchanged
- Keep only the ninth bit and drop the low 8 bits
- Keep the low 8 bits and wrap, or report an error
Ana writes 1112 for 1111 + 1. Which correction is needed?
- Binary has no digit 2, and carrying gives 10000.
- She lined up the numbers on the wrong side before adding.
- Nothing is wrong, because 1 + 1 makes 2 in every base.
In 8-bit storage that keeps only the low 8 result bits, what happens when 255 + 1 is stored?
- 256 is stored safely as an ordinary 8-bit value, with no extra bit.
- 0 remains when the extra carry is discarded from the 8-bit result.
- The program always crashes before storing the result in memory.

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 · Binary has only 0 and 1. In one column, 1 plus 1 gives 0 in that column and a carry of 1 to the left.
Left one column · A carry joins the next column to the left before that column is added.
Yes. The sum is 11000111, which is 199. · The binary sum is 11000111. That is 199, and 199 is within the unsigned 8-bit range 0 through 255.
256 · Eight bits give 256 patterns, counting 0 up to 255.
Keep the low 8 bits and wrap, or report an error · If the ninth bit is not stored, the low eight bits remain and the value can wrap. Some programs report the overflow instead or choose a larger type.
Binary has no digit 2, and carrying gives 10000. · Binary digits are only 0 and 1. The carry moves left through all four 1s, giving 10000.
0 remains when the extra carry is discarded from the 8-bit result. · 255 plus 1 is 256, written 1 followed by eight zeros. When only eight result bits are kept, the leading 1 is discarded and 0 remains.