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// Create a 4-bit type called Nybble using System; // A 4-bit type class Nybble { int val; // underlying storage public Nybble() { val = 0; } public Nybble(int i) { val = i; val = val & 0xF; // retain lower 4 bits } // Overload binary + for Nybble + Nybble public static Nybble operator +(Nybble op1, Nybble op2) { Nybble result = new Nybble(); resultval = op1val + op2val; resultval = resultval & 0xF; // retain lower 4 bits return result; } // Overload binary + for Nybble + int public static Nybble operator +(Nybble op1, int op2) { Nybble result = new Nybble(); resultval = op1val + op2; resultval = resultval & 0xF; // retain lower 4 bits return result; } // Overload binary + for int + Nybble public static Nybble operator +(int op1, Nybble op2) { Nybble result = new Nybble(); resultval = op1 + op2val; resultval = resultval & 0xF; // retain lower 4 bits return result; } // Overload ++

Part I:

We apply l H opital s Rule one last time to obtain = lim 24(x 2) = 0 x 2 cos(x 2)

public static Nybble operator ++(Nybble op) { Nybble result = new Nybble(); resultval = opval + 1; resultval = resultval & 0xF; // retain lower 4 bits return result; } // Overload > public static bool operator >(Nybble op1, Nybble op2) { if(op1val > op2val) return true; else return false; } // Overload < public static bool operator <(Nybble op1, Nybble op2) { if(op1val < op2val) return true; else return false; } // Convert a Nybble into an int public static implicit operator int (Nybble op) { return opval; } // Convert an int into a Nybble public static implicit operator Nybble (int op) { return new Nybble(op); } } class NybbleDemo { static void Main() { Nybble a = new Nybble(1); Nybble b = new Nybble(10); Nybble c = new Nybble(); int t; ConsoleWriteLine("a: " + (int) a); ConsoleWriteLine("b: " + (int) b); // Use a Nybble in an if statement if(a < b) ConsoleWriteLine("a is less than b\n"); // Add two Nybbles together c = a + b; ConsoleWriteLine("c after c = a + b: " + (int) c);

9:

// Add an int to a Nybble a += 5; ConsoleWriteLine("a after a += 5: " + (int) a);

ConsoleWriteLine(); // Use a Nybble in an int expression t = a * 2 + 3; ConsoleWriteLine("Result of a * 2 + 3: " + t); ConsoleWriteLine(); // Illustrate int assignment and overflow a = 19; ConsoleWriteLine("Result of a = 19: " + (int) a); ConsoleWriteLine(); // Use a Nybble to control a loop ConsoleWriteLine("Control a for loop with a Nybble"); for(a = 0; a < 10; a++) ConsoleWrite((int) a + " "); ConsoleWriteLine(); } }

(f) limx 1 (e x 1) = 0 and limx 1 (x 1) = 0 so l H opital s Rule does not apply In fact the limit does not exist 2 (a) limx + x 3 = limx + (e x 1 x x 2 /2) = + Rule applies Thus so l H opital s

Brad found himself correcting several grammatical errors at the same time that he worked to shorten sentences Brad s latest version dropped from 272 words to 249 words, a reduction of more than 8 percent There are eighteen sentences If you divide 272 words by eighteen sentences, you get an average sentence length of a little over fteen words Brad said, That s great How about your draft What s your average sentence length If it s longer than twenty words, did you rewrite to lower your average

The output from the program is shown here:

a: 1 b: 10 a is less than b c after c = a + b: 11 a after a += 5: 6 Result of a * 2 + 3: 15 Result of a = 19: 3 Control a for loop with a Nybble 0 1 2 3 4 5 6 7 8 9

Although most of the operation of Nybble should be easy to understand, there is one important point to make: The conversion operators play a large role in the integration of Nybble into the C# type system Because conversions are defined from Nybble to int and from int to Nybble, a Nybble object can be freely mixed in arithmetic expressions For example, consider this expression from the program: