Binary Math for Beginners

In everyday life, we are used to the decimal system — we have ten digits from 0 to 9. If we add 5 and 6, we get 11: there is no longer room for a single-digit answer, so we carry the one to the next place (the tens).

The computer does exactly the same thing, but it only has two digits: 0 and 1. Addition in binary looks very simple:

• 0 + 0 = 0
• 1 + 0 = 1

But 1 + 1 equals 2, and the computer has no digit "2"! So a place overflow occurs: two is written as 10. The computer writes 0 in the current place and carries the one to the next — just like we carry tens when doing column addition. Understanding this simple overflow principle is the key to teaching silicon chips to truly count.

Practical example. Let's add 3 and 5 in binary. 3 is 0011, 5 is 0101. We add bit by bit from right to left: 1+1=0 carry 1; 1+0+1(carry)=0 carry 1; 0+1+1(carry)=0 carry 1; 0+0+1(carry)=1. Answer: 1000 — that's 8. This is exactly how a cascade of adders works in a processor: each bit is added separately, and the carry is passed to the left neighbor, just like in elementary school column addition.