Numbers How does computer understand numbers? Knows only two symbols We are mostly familiar with decimal numbers General number representation in arbitrary base An algorithm for converting between bases Special case: base=2 (binary) Is there a decimal to binary converter inside the computer? Compiler does it Negative numbers? Two representation conventions: sign-magnitude representation and 2’s complement representation

2’s complement Steps involved in converting decimal to 2’s complement Decide the number of bits (should be at least 2+integer part of log2|N|) Write the magnitude in binary and append zeros at the front to fill up the remaining bits (this is 2’s complement of the positive number) Flip all bits (this is 1’s complement of the positive number) Add 1 to it (this is 2’s complement representation of the negative number)

2’s complement 2’s complement to decimal: Write down the polynomial expansion in base 2 Append a negative sign to the leading coefficient Comparison of 2’s complement and sign-magnitude Range in sign-magnitude with n bits Range in 2’s complement with n bits Benefits of 2’s complement in binary arithmetic: will discuss later All computers and calculators use 2’s complement representation

if statement if (condition) { statements } Nested if if (condition1) {

/* Compute density and prevent division by zero */ class densityIf { public static void main (String args[]) { double mass, volume, density; mass = 27.2; volume = 0.0; density=0.0; if(volume<=0.0) System.out.println("Density cannot be computed as the volume is zero"); if(volume>0.0) System.out.println("Density of the liquid is: "+ mass/volume); }

Nested if Sometimes possible to simplify nested if if (condition1) { statements } Same as if ((condition1) && (condition2)) {

Example class exampleIf { public static void main(String arg[]) { int x=10, y, z; if ((x%2)==0) {System.out.println(x + “ is even.”); if ((x%3)==0) {System.out.println(x + “ is a multiple of 6.”); y = x/6; } z = x%6;