Suppose we have a counter that stores an arbitrary number of bits and counts in binary. It always begin at 0. The only mutator operation it can perform is to increment, adding one to the current count. This changes one or more bits. Show that if we start at 0 and perform k increment operations, a total of O(k) bits will change. Hint 1: If you are stuck, count to 20 in binary on paper. After each increment, write how many bits have changed. See if you notice a pattern. Hint 2: Whenever you add one, give it some credit, similar to the analysis of expansion in lecture 7.

Why is hard disk space important to an audio engineer? why are usb ports and firewire ports useful for an audio engineer? explain in 2-3 sentences. (3.0 points) here's a list of different audio software: ableton live apple inc.'s garageband apple inc.'s logic studio digidesign's pro tools propellerhead sofware's reason sony creative software's acid pro steinberg cubase steinberg nuendo choose one of the software programs listed above, and then go to that software program's web site. read about what the software program is used for, and then write 4-5 sentences about what you learned. (10.0 points) which type of software license is the most limiting? why? explain in 2-3 sentences. (3.0 points) when sending a midi channel voice message, how can you control the volume of the sound? explain in 2-3 sentences. (4.0 points)