Consider the sequence (7,7,7,6,6,4,4,3). (a) perform the reduction operation repeatedly until a sequence con- taining negative numbers appears. (b) is the sequene obtained graphic? why/why not? use the theorem to determine whether the original sequence is graphic or not. (c) assume, for some graph, the repeated reduction operation produces the sequence (2) or (4,0). is either of these graphic? what can you conclude about the original sequence?

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

1. package newton’s method for approximating square roots (case study 3.6) in a function named newton. this function expects the input number as an argument and returns the estimate of its square root. the script should also include a main function that allows the user to compute square roots of inputs until she presses the enter/return key. 2. convert newton’s method for approximating square roots in project 1 to a recursive function named newton. (hint: the estimate of the square root should be passed as a second argument to the function.) 3. elena complains that the recursive newton function in project 2 includes an extra argument for the estimate. the function’s users should not have to provide this value, which is always the same, when they call this function. modify the definition of the function so that it uses a keyword parameter with the appropriate default value for this argument, and call the function without a second argument to demonstrate that it solves this problem. 4. restructure newton’s method (case study 3.6) by decomposing it into three cooperating functions. the newton function can use either the recursive strategy of project 1 or the iterative strategy of case study 3.6. the task of testing for the limit is assigned to a function named limitreached, whereas the task of computing a new approximation is assigned to a function named improveestimate. each function expects the relevant arguments and returns an appropriate value. 5. a list is sorted in ascending order if it is empty or each item except the last one is less than or equal to its successor. define a predicate issorted that expects a list as an argument and returns true if the list is sorted, or returns false otherwise. (hint: for a list of length 2 or greater, loop through the list and compare pairs of items, from left to right, and return false if the first item in a pair is greater.)

[a] create a class called “cycle” which has two instance integer variables as properties, “numberofwheels” and “weight.” create a constructor with two parameters, using the same variable names in the parameter list. assign each variable to numberofwheels” and “weight” respectively. write a separate application to test the class and display its properties. note: do not change the names of the instance variables or the variables listed in the constructor’s parameter list. [b] edit your class cycle by adding a default constructor which will assign the default values of 100 to represent the numberofwheels, and 1000 to represent the weight, by invoking a call to the other constructor. modify your application created in [a] to test the class.