Decoding Binary: Converting to Decimal

In our everyday lives, we use the Decimal system (Base-10), which relies on ten digits (0-9). Computers, however, use the Binary system (Base-2), which only uses 0 and 1. The secret to reading binary is understanding Place Value. In decimal, each column is a power of 10 ($1, 10, 100$). In binary, each column is a power of two. We read binary from right to left, starting with $2^0$. Each step to the left doubles the value: $1, 2, 4, 8, 16, 32, 64, 128$. These are the 'slots' where we place our 1s and 0s.

Think of each binary digit (or bit) as a light switch. A 1 means the switch is 'On,' and we count that column's value. A 0 means the switch is 'Off,' and we ignore that value. To convert a binary string to decimal, you simply look at which 'switches' are on and add their corresponding powers of two together. For example, in the 4-bit number $1010$, the '8' switch and the '2' switch are on. By adding them ($8 + 2$), we find the decimal value is $10$.