Each Student's Unique Binary Number at Enrollment

Binary Arithmetic in Student ID Number Assignment

Each student that enrolls at a school is assigned a unique ID number, which is stored as a binary number. The ID numbers increase sequentially by 1 with each newly enrolled student. If the ID number assigned to the last student who enrolled was the binary number 1001 0011, what binary number will be assigned to the next student who enrolls?

Response: 1001 0100

Binary arithmetic is essential in determining the student's number. The binary notation, used by computers to perform calculations, works based on the elements 0 and 1. In simple addition:

0 + 0 = 0

1 + 0 = 1

0 + 1 = 1

1 + 1 = 10 (carry over the 1)

By applying binary arithmetic, the number assigned to the next student after 1001 0011 is 1001 0100. The sequence follows the binary system rules where each digit has only two possible outcomes.

Why do we use binary arithmetic in computers?

Binary arithmetic is utilized in computers because it simplifies their operations. With only two possible outcomes for each digit (0 or 1), storing and manipulating numbers becomes more efficient compared to the decimal system where there are 10 possible outcomes for each digit.