### Recitation 03: Integers

• Integers and Twos Compliment Representation.
• If we have a binary number with n bits represented as $b_{n-1}b_{n-2} \ldots b_2b_1b_0$, we can calculate its decimal value as: $$-b_{n-1} \times 2^{n-1} + \sum_{i=0}^{n-2} b_i \times 2^i$$
• To reinforce the modular arithmetic properties of ints, we can visualize the points as lying along the edge of a circle. Example. Credit to Josh Zimmerman for this example.
• A few slides borrowed from 15-213 with some helpful graphics to help visualize int properties.
• Discussed bitwise not (~) and the property that $-x = \sim x + 1$.

If you have any comments or see any errors, please let me know.