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Decimal numbers are in base 10 and binary numbers are in base 2. Let's take the number 135. This is equal to 100 + 30 + 5. Or 1 * 10^2 + 3 * 10^1 + 5 * 10^0. (the caret being the sign for exponent and any number greater than 0 to the exponent 0 equal 1 hence 10^0 = 1). In binary format, the base is two so the first basic number is 2^0 = 1, then 2^1 = 2, then 2^2 = 4 and so on, 8, 16, 32, 64...

to build a number like 135 in binary you may ask how many 2^8 = 256 can I fit in it? The answer is 0, then how many 2^7=128, the answer is 1. Having already allocated 128 in the number, there is only a value of 7 left to insert. That is to say that there won't be any 2^6, 2^5, 2^4, or 2^3 in it. Since 2^2 = 4 and that fits into the remaining 7 we put 1 of those. We do the same for 2^1=2 and 2^0=1 and we have the final value (0*2^8) + (1*2^7) + (0*2^6) + (0*2^5) + (0*2^4) + (0*2^3) + (1*2^2) + (1*2^1) + (1*2^0) or using only the coefficients: 010000111. Since the first zero is irrelevant, 135 in binary is 10000111!

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โˆ™ 2011-09-12 20:19:40
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Related questions

Convert the following decimal numbers into their equivalent binary numbers and then convert the resulting binary numbers back into the decimal numbers a. 6401 b. 1010110?

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Prime numbers are prime numbers - whether we count in the decimal, binary, hexadecimal or another base.


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What is the binary number of 209.85.153.94?

Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).


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