Understanding the Decimal and Binary Number Systems

1. How the Decimal Number System Works

The decimal number system is the one we use in everyday life. It is a base-10 system, meaning it uses ten digits: 0 through 9.

The choice of ten as the base is historically tied to the fact that humans have ten fingers, which made it natural to count this way.

Breaking Down a Decimal Number

Let’s analyze the decimal number 831:

• Each digit has a place value based on its position
• The further to the left, a digit is, the greater its significance because it is multiplied by higher powers of 10

We can decompose 831 as follows:

• The digit 8 is in the hundreds place: 8 × 10² = 800
• The digit 3 is in the tens place: 3 × 10¹ = 30
• The digit 1 is in the ones place: 1 × 10⁰ = 1

Adding these together gives: 8800 + 30 + 1 = 831

2. Understanding the Binary Number System

In computers, information is stored as a series of bits, which can only have two values: 0 and 1.