Welcome to the binary number system! Binary is a base-2 number system that uses only two digits: zero and one. Think of it like a set of cards, where each card represents a power of 2. The rightmost card has 1 dot representing 2 to the power of 0, the next has 2 dots for 2 to the power of 1, then 4 dots for 2 to the power of 2, and 8 dots for 2 to the power of 3.
Now let's convert the binary number 1011 to decimal. Each position represents a power of 2, and we only count the positions where the digit is 1. Starting from the left: the first 1 is in the 8s place, the 0 means the 4s place is off, the next 1 is in the 2s place, and the final 1 is in the 1s place. So we add: 8 plus 0 plus 2 plus 1, which equals 11 in decimal.
Now let's convert decimal 13 to binary. We start with the largest power of 2 that fits into 13. Can we use 8? Yes, because 13 is greater than or equal to 8. So we turn on the 8s card and have 5 remaining. Can we use 4? Yes, 5 is greater than 4. Turn on the 4s card with 1 remaining. Can we use 2? No, 1 is less than 2, so the 2s card stays off. Can we use 1? Yes! Turn on the 1s card. Reading from left to right: 1101 in binary equals 13 in decimal.
Let's see how binary counting works from 0 to 15. Notice the pattern: the rightmost digit alternates between 0 and 1 with each count, the next digit changes every 2 counts, the third digit changes every 4 counts, and the leftmost digit changes every 8 counts. This creates a systematic pattern where each position represents a power of 2, making binary counting very logical and predictable.
To summarize what we've learned about binary: Binary is a base-2 number system using only 0 and 1. Each position represents a power of 2, like switches that can be on or off. This simple system is the foundation of all computer operations, and converting between binary and decimal follows logical, predictable rules.