i. At the Very Large Array in Soccorro, New Mexico, you receive a strange transmission coming from the star Vega, 25 light-years away. It is a sequence of numbers: -35, -9, -9, -1 which keeps repeating. Everyone is stumped until you suggest converting the numbers into four 8-bit 2s-complement numbers and sequencing them together to form a single 32-bit binary sequence. Have you discovered an alien intelligence? Explain your answer by identifying the resulting pattern. (Hint, write down a sequence of numbers denoting the number of sequential ones. What is this sequence? Is it likely to be naturally occuring?

ii. While on your next assignment at the Arecibo Radio Observatory in Puerto Rico, you get the following message coming from Proxima Centauri, the closest star (other than the Sun) to Earth at 4.22 light-years. The message reads: 0, 87, 82. 114, 82, 82, 87, 0. This time a single long binary sequence doesnt work. Try stacking the 8-bit binary representations to form an 8x8 pixel array (1=ON, 0=OFF). What is the message?

iii. Your fame as an exobiologist is secured! At Roswell, New Mexico, you are asked to examine a technical journal from an alien crash site. One strange equation reads: 412 + 156 = 601. Assuming this equation is correct, and their counting system is based on the number of fingers they have, how many fingers would you expect the aliens to have? Try to derive your result algebraically rather than just guessing and verifying. Let b = the base, with the digit places representing powers of b: b 0 , b 1 , b 2 , etc.