Do you want to learn how floating point numbers are stored in the computer?
Even if you have a good grasp of binary numbers, most people still have no idea how a floating point number is stored in their computer. This app will let you explore “floats” and give you a firm understanding of what the computer really remembers when you put in 3.1415927.
In this app you can enter a number and see the floating point representation, and the smallest increment that you can change the number by. You can also edit the exponent or significant figures separately.
If you don’t understand binary numbers too well, then this can help you learn about binary, hex and dec numbers. All three text boxes take either hex or decimal inputs. You can also hit the “add one” buttons to watch the computer count up in binary.
If you want to change individual bits, you can tap them to toggle their values, and all of the displayed numbers are updated accordingly.
Finally, you can see how to get from the parts to the final number. The formula that the computer uses to add your numbers together is displayed at the bottom.
There is no shame in not understanding floating point numbers. I recently discussed this idea with a few very technically inclined individuals, including someone who has been a full time programmer for 45 years, and none of them could explain what a floating point number actually looks like. Now you can use “Explain Floats” to learn about how the computer stores your data, and get a good understanding of the rounding errors that you will see when doing floating point math. Are you using floating point numbers to calculate averages? You should know that sometimes adding to a floating point number does nothing at all. Take a look at Explain Floats to see how this all works.
This app displays and uses 32 bit floating point numbers. “Doubles” are basically the same, but with twice as many bits.