Binary/Decimal Converter

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Binary to Decimal
Decimal to Binary

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Convert Binary Numbers to Decimal

This free online binary to decimal and decimal to binary converter allows you to automatically convert huge numbers to their decimal or binary equivalent. Enter up to 50,000 binary digits (bits) or decimal digits and get the equal decimal/binary value. When you convert base-2 binary numbers to their equivalent base-10 decimal number with this tool, you can choose to include spaces in the number, eg: "1011 1001 0111", or you can enter the number without spaces, eg: "101110010111". Decimal numbers are also automatically stripped of commas and spaces, so you can enter a number in any of these ways: "1,230,300", "1 230 300", "1230300".

How to convert binary numbers to decimal

You can automatically convert binary to decimal with this app by simply entering your binary number in the text box and clicking convert. Or you can do it manually using a pretty simple technique: Looking from left to right at the binary number, starting with the first "1", first multiply the running total of the decimal number (starting at 0) by 2, then if the binary digit (bit) is 1, add 1 to the decimal value. Repeat with each digit in the binary number. For more conversion techniques, you can read this wikihow article, and this Ohio State handout.

How to convert decimal numbers to binary

You can automatically convert decimal to binary with this app as well simply by choosing the decimal to binary option prior to copying and pasting your number in the box and selecting the convert button. You can also manually convert decimal numbers to binary using techniques described in this other wikihow article, and this electronics tutorial. Essentially you would do the following: divide the number by 2, if there is a remainder, append 1 to the binary number. If their is no remainder, append a 0. You then repeat this process until the total is 0 and you have a converted number. One last step is to flip the result to get the true binary number. Or to not need this step, write it from right to left to begin with.

Why convert numbers?

Binary (base-2) is most commonly used in computer systems, digital circuitry, and modern electronic devices like smart phones. Whether working with hardware, coding software or just working with raw numbers and mathematics, many people find the need to automatically convert from one base to another, or to just check their work after having manually done the conversion. For more info on the binary number system see this wikipedia article.