Although we are most familiar with base-10 numbers, this is not the only system of numbers that is used. Computers have three other number systems that it uses: binary (base-2), octal (base-8), and hexadecimal (base-16). We are going to explore those bases to understand how they work.
The primary difference is that the size of rods and trays are different. When working in base-10 it takes 10 pieces to go up to the next shape. In base-8 it only takes 8. Here is the visual representation of the number \(127_8\text{.}\)
Determine what this number is in base-10 and explain your logic.
2.
Converting numbers from base-10 to base-8 is a bit more complicated. Try to imagine that you have a bunch of loose blocks that you’re filling into different trays that are built around the number 8 instead of the number 10. Work from the largest trays and work your way down.
Convert 89 to base-8 and explain your process in words.
3.
Using the logic that you developed, convert 14 to base-2 and explain your process in words.
