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Problems: 1. using textbooks, reference books, and internet as your source of research, draw the following microprocessor microarchitectures i. intel 8086 ii. motorola 68000 i atmel atmega32 iv. mips single cycle v. arm cortex-m3 write an hdl module for a hexadecimal seven-segment display decoder. the input is 4-bit binary representing a hex number (0-f), and the output is 8-bit seven segment display bits (a-h). thus, the decoder must handle the digits 10 - 15 to display a-f respectively, in addition to 0-9 numbers. 2. design a 4-bit left and right rotator (both outputs). first sketch schematic diagrams of your design. then implement your design using hdl coding. 3. 4. design a modified priority encoder that receives an 8-bit input, a7: 0 and produces a 3-bit output, y2o. y indicates the most significant bit of the input that is true. y should be 0 if none of the inputs are true. give a simplified boolean equation, sketch a schematic, and write an hdl code. 5.write an 8: 1 multiplexer module called mux8 with selection inputs s, data input d, and data output y. data input (d) and data output (v) are 32-bit wide

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.

Consider a slotted aloha system, where the time slot equals the fixed duration of each packet. assume that there are 4 stations a,b,c,d sharing the medium. (a) stations a,b,c,d receive one packet each from higher layers at times 1.3, 1.5, 2.6,5.7 respectively. show which transmissions take place when, according to the slottedaloha protocol; describe all transmissions until all four packets have been successful.when needed, each station has access to the following sequence of random number, provided by a random number generator and drawn uniformly between 0 and 1: (1) station a draws numbers: 0.31, 0.27, 0.78, 0.9, 0.9, 0.11, 0. (2) station b draws numbers: 0.45, 0.28, 0.11, 0.83, 0.37, 0.22, 0. (3)station c draws numbers: 0.1, 0.2, 0.3, 0.4, 0. (4) station d draws numbers: 0.36, 0.77, 0.9, 0.1, 0.1, 0.1, 0.1, 0. (b) in slotted aloha, a station transmits in each time slot with a given probability. what probabilities would you assign to each of the four stations so as to: (i) maximize the efficiency of the protocol? (ii) maximize fairness among the four stations? (c) will the efficiency increase or decrease if we modify slotted aloha as follows: (i) get rid of slots and allow stations to transmit immediately? (ii) implement carrier sensing? (iii) implement collision detection? (iv) implement collision avoidance?