Write the half function. a function call and the functionprototype
are provided.
void half(float *pv);
float value=5.0;
printf("value before half: %4.1f\n",value); // prints 5.0
half(& value);
printf("value after half: %4.1f\n",value); // prints 2.5

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

Howard is designing a chair swing ride. the swing ropes are 5 meters long, and in full swing they tilt in an angle of 29° outside chairs to be 2.75 m above the ground in full swing.

Consider a direct-mapped cache with 216 words in main memory. the cache has 16 blocks of 8 words each. it is a word-addressable computer (rather than a byte-addressable computer which we normally discuss). (a) how many blocks of main memory are there? (b) what is the format of a memory address as seen by the cache, that is, what are the sizes of the tag, cache block, and block offset fields (if they apply)? (c) to which cache block will the memory reference db6316 map?