AP CSP Day 52: Binary Arithmetic & Overflow
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Big Idea 2
Day 52 Practice
Focus: Binary Arithmetic & Overflow
Practice Question
A computer stores unsigned integers using 8 bits. What happens when you add 255 + 1?
Why This Answer?
8 bits can represent 0-255. 255 = 11111111 in binary. Adding 1 causes overflow, wrapping around to 00000000 = 0.
Why Not the Others?
A) 256 requires 9 bits, can't store in 8 bits.
C) Overflow happens silently in most systems.
D) -1 requires signed integers, question specifies unsigned.
Common Mistake
Watch Out!
Not recognizing overflow behavior. With fixed bits, adding beyond maximum wraps to minimum.
AP Exam Tip
Overflow: adding past maximum value wraps to minimum. Example: 8-bit unsigned: 255 + 1 = 0.