Q&A for How to Convert from Binary to Decimal

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  • Question
    How do you convert a negative decimal to binary?
    wikiHow Staff Editor
    Staff Answer
    This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.
    wikiHow Staff Editor
    Staff Answer
    First, ignore the decimal sign and keep dividing the number by 2 until the quotient is 0, always writing down the remainder to the right of each quotient. Write down the remainders from bottom to top of the list to make a sequence of 1s and 0s, and divide the list up into groups of 4, starting at the end. Add extra 0s to the front of the list if you have to. To convert the binary representation into a negative number, “flip” the sequence so that each 0 becomes a 1 and each 1 becomes a 0. Add 1 to the sequence to get your final answer. Remember that 1 + 1 = 10 in binary.
  • Question
    Can you convert from binary to hexadecimal?
    wikiHow Staff Editor
    Staff Answer
    This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.
    wikiHow Staff Editor
    Staff Answer
    Yes. Binary is base 2, while hexadecimal is base 16. Hexadecimal numbers can be represented as the numbers 0-9 and the letters A-F (for numbers greater than 10). You’ll need to take a binary line of 4 numbers and multiply the numbers by 1, 2, 4, and 8, respectively, going from right to left. Add the results together to get your answer.
  • Question
    What is 11100.1010 binary in decimal?
    Community Answer
    1x2^4 + 1x2^3 + 1x2^2 + 0x2^1 + 0x2^0 + 1x2^-1 + 0x2^-2 + 1x2^-3 + 0x2^-4 = 29.6250
  • Question
    How can I do it in a simpler way?
    Donagan
    Top Answerer
    It actually doesn't get any simpler than what is shown above.
  • Question
    How do you convert from decimal to binary?
    Community Answer
    If you're using small numbers, like below 256, you can easily figure it out without much of a technique. Just take a number like 50: The binary system is 128 64 32 16 8 4 2 1. Work from left to right checking if the number of the binary system will fit into your number, so the first would of 32 for 50. From this we know the start of the binary number: 001. If you take away 32 from 50 you will get 18, which will need to be formed from the remaining binary number, so check from left to right again, and you find that 16 fits in, so the start of the number is 0011, and we have 2 left over, so we can find the binary number as 0011 0010.
  • Question
    Why do we put base subscript?
    Donagan
    Top Answerer
    It's a convenient way to help prevent confusion when working with bases other than ten.
  • Question
    How do I decide the base value?
    Community Answer
    The base value is always 2 in binary, as there are 2 numbers used in the system. In decimal, 10 numbers are used, so 10 is the base value.
  • Question
    What is D2 in a binary?
    Community Answer
    If D2 = decimal 2, then the binary would be 10 with base 2. If D2 = hexidecimal, then the binary would be 11010010 with base 2.
  • Question
    How can I covert 64 to a binary system?
    Community Answer
    By reversing the rules above, you get 01000000.
  • Question
    What is the meaning of "b" in this number "0b1010"?
    Cluster_Ducky
    Community Answer
    It is a prefix that helps a computer identify what base the digits are in. Here are a few examples: "0b" = binary form, "0x" = hexadecimal, "0d" = denary.
  • Question
    How do I multiply with positional values?
    Donagan
    Top Answerer
    Multiply the positional value (1, 2, 4, 8, etc.) by the digit (0 or 1) in that position. You do the same thing with numbers in base-ten or any other base.
  • Question
    Convert 101110 to decimal number.
    Hunaid Khan
    Community Answer
    It is 46. 101110 = (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰) = 46.
  • Question
    The example in #10 is confusing me. 1 X 37 + 2 = 39, doesn't it?
    Community Answer
    Yes. It should be, and the next line is also wrong. Both times the 38 should be 39. The final answer of 1446 is correct because it's 39*37 + 3.
  • Question
    What is 1011111 in decimal Number
    Tinkerer02
    Top Answerer
    Using powers of 2, we get 1x2^6 + 0x2^5 + 1x2^4 + 1x2^3 + 1x2^2 + 1x2^1 + 1x2^0 = 64+0+16+6+4+2+1 = 95 in decimal. Using doubling, we get: 0x2+1 = 1; 1x2+0 = 2; 2x2+1 = 5; 5x2+1 = 11; 11x2+1 = 23; 23x2+1 = 47; 47x2+1 = 95, which is the same as the powers of 2 method.
  • Question
    The doubling example of 123 base 37 2nd step must be 39, isn't it? 1x37+2=39. 39x37+3=1446.
    Tinkerer02
    Top Answerer
    Yes, there is a mistake on the diagram. It should be: 0x37+1=1. 1x37+2=39. 39x37+3=1446. 123 base 37 = 1446 base 10.
  • Question
    What is the highest decimal that can be written in binary?
    Tinkerer02
    Top Answerer
    For unsigned integers, It is 2n-1, where n is the number of bits in the binary number. So for 16 bits, it is 1111 1111 1111 1111 = 65536 - 1 = 65535. For 32 bits, it is 232-1 = 4,294,967,296 - 1 = 4,294,967,295. For 64 bits, it is 232-1 = 18,446,744,073,709,551,616 - 1 = 18,446,744,073,709,551,615. For signed integers, the largest positive number is 2n-1 -1. We have n-1 bits because the highest bit is used for negative numbers, and we count the 0s instead of the 1s. This is called 2's complement notation. The smallest negative number is then 2n-1 * -1. For 32 bits, we get 2,147,483,647 and -2,147,483,648, respectively.
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