Adding Binary Numbers
(Really) Old Things Made New…
Recall that when you first learned to add multi-digit numbers such as \(1124\) and \(597\), you needed to “carry” a \(1\) to the next place-value when the sum of the digits in each column was greater than or equal to 10 (i.e. the base). Viz:
It turns out that if we want to add binary numbers, we can use exactly the same method, but carrying the \(1\) when the sum of the bits in each column are greater than or equal to \(2\).
It is important to note that, in binary \(1+1=10\) because the “\(10\)’s digit” represents a 2. So the binary number \(10_2\) essentially states that you have “one \(2\), and zero \(1\)’s” because each place-value in a binary number is a power of \(2\) (instead of the usual \(10\) in base 10).