you want to find a single word, for example, that starts with a letter p, you will open the dictionary in the middle and find out that you are in the section with the letter m. you know that letter p is further in an alphabet, so you can forget about the first half of a dictionary. by doing it, we are cutting our input in half and we are left with a range of letters from m to z. so now, we jump into the middle of our range, and we will find the letter s. we know that p is before s, so we are left with the 