AQA A-Level Computer Science: Fundamentals of the Binary Number System

AQA A-Level Computer Science: Fundamentals of the Binary Number System

Introduction

The binary number system is the foundation of all modern computing. It uses only two digits, 0 and 1, to represent data. This might seem limited, but its simplicity allows computers to process information incredibly efficiently.

Representing Data with Binary

Imagine a light switch. It can be either ON or OFF. In binary, 1 represents ON and 0 represents OFF. This "ON/OFF" concept is fundamental to how computers work. Transistors, tiny electrical switches within computer chips, are constantly switching ON or OFF, creating combinations of 1s and 0s that represent data.

Binary-to-Decimal Conversion

You're likely familiar with the decimal number system (base-10) where we use digits 0 through 9. To understand binary, we need to convert between the two systems.

Each digit in a binary number has a place value that is a power of 2. Starting from the rightmost digit:

• 20 = 1
• 21 = 2
• 22 = 4
• 23 = 8
• ... and so on.

Example:

Let's convert the binary number 1011 to decimal:

• 1011
• 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20 = 8 + 0 + 2 + 1 = 11

Therefore, the binary number 1011 is equivalent to the decimal number 11.

Basic Binary Arithmetic

Addition:

Binary addition works similarly to decimal addition, but with only 0s and 1s.

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 10 (carry-over)

Example:

   1011
+  0101
-------
   1100

Subtraction:

Binary subtraction is a bit more involved. You may need to borrow from the next digit, similar to decimal subtraction.

Example:

   1011
-  0101
-------
    110

Conclusion

Understanding the binary number system is essential for anyone studying computer science. It allows us to comprehend how computers represent and manipulate data. This tutorial has provided a basic introduction to binary, including its conversion to decimal and basic arithmetic.