To convert a binary number displayed on the odometer back to decimal you could roll the odometer back one tick at a time, counting aloud until the odometer reads "00000000". Since you understand how the odometer rolls forward you'll also understand how it rolls backward, too. Whatever is displayed on the odometer after all that counting and rolling would be the binary representation of the decimal number you counted up to. To convert a decimal number to binary you could roll the odometer forward, tick by tick, counting aloud until you've rolled it a number of times equal to the decimal number you want to convert to binary. It's exactly the same as a traditional decimal odometer's operation, except that each digit can only be "0" or "1" on our fictional "binary odometer". You can memorize all of that if you want, but you really only need to understand how the little odometer "rolls over" as the number it's counting gets bigger. That's the binary representation of the decimal number 4. The number "11", in binary notation, is the same as the decimal number 3.įinally, when you've driven your fourth mile both digits (which were reading "1" at the end of the third mile) roll back over to zero position, and the 3rd digit rolls up to the "1" position, giving us "00000100". When you've driven the third mile the odometer reads "00000011", since the first digit of the odometer turns again. This looks like the number 10 in decimal notation, but it's actually 2 (the number of miles you've driven the car so far) in binary notation. When you've driven your second mile the first digit of the odometer rolls back over to "0" (since its maximum value is "1") and the second digit of the odometer rolls over to "1", making the odometer read "00000010". When you've driven your first mile the odometer reads "00000001". When the car is fresh from the factory the odometer reads "00000000". Think of a car's "odometer", except that unlike a traditional odometer each digit can only count up to 1 from 0. You really should know how to do it.Ĭounting in binary is so simple because you only have to know how to count to 1! It's really, really easy to learn to count in binary, and to learn shortcuts to convert binary to decimal and back. If you are already fluent in binary (base 2) notation you can skip this section.įor those of you who are left: Shame on you for not being fluent in binary notation! Understand how those decisions work, and you can understand how to plan IP subnets. Simply put, though, IP routers use your IP subnets to make routing decisions. You can use IP subnets to break up larger networks for logical reasons (firewalling, etc), or physical need (smaller broadcast domains, etc). IP subnets exist to allow routers to choose appropriate destinations for packets.
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