So we get back to where we started after doing this twice. When we encrypt, we add one copy of some bit string to our input. If we go back to the fact that the XOR operation is like adding bits mod 2, then the above magic trick becomes very clear. Try it yourself in the app above! We will use this fact in assignment 2 to encrypt data. Notice that if you XOR a bit string with the same bit string twice, you get back to where you started. Or, in other words, return the sum of the two bits mod 2īelow is a little applet where you can interactively examine what the binary bitwise operators yield for different inputs XOR: Return a 1 if exactly one input bit is a 1.OR: Return a 1 if at least one input bit is a 1.AND: Only return a 1 if both input bits are 1.In plain English, here's what this is saying: They apply on corresponding bits on binary strings as follows: There are also three binary bitwise operators we'll need to worry about in this class. The binary not operator, denoted by ~ in C++, changes all of the 1's to 0's and all of the 0's to 1s In fact, this is the fastest possible way to do this on your computer. Number of applications of num = num > 1 Īs you can see, the right shift is equivalent to dividing by 2 and discarding the remainder (or, equivalently, integer dividing by 2). Below is an example of repeatedly applying the right shift operator to the number 174 in C++ The left shift, denoted by > in C++ deletes the rightmost bit and shifts every other bit over to the right. The ones we'll mainly use in the course are the shift operators.

Let's start with the unary operators on binary strings. But we're going to define some operators now that are unique to binary bit strings. 5 is 'negative 5'), and a binary operator is addition (e.g. For example, a unary operator is the - sign (e.g. We're used to operators in ordinary arithmetic.

Binary bitwise operators: These are functions that take in a pair of binary numbers and return another one.

Unary bitwise operators: These are functions that take in a binary number and return another one.

In addition to understanding how to represent numbers in binary and hex, we also need to learn two types of binary operators:

Linear feedback shift register uwn