Converter of unsigned binary (base two): converting to decimal system (base ten) unsigned (positive) integer numbers

Convert unsigned binary numbers (base two) to positive integers in the decimal system (base ten)

How to convert an unsigned binary number (base two) to a positive integer in base ten:

1) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

2) Add all the terms up to get the integer number in base ten.

Latest unsigned binary numbers converted to positive integers in decimal system (base ten)

11 0011 1010 1011 1110 1001 = 3,386,345 Sep 28 09:35 UTC (GMT)
1011 0001 0110 1000 0000 0000 0000 0011 = 2,976,382,979 Sep 28 09:34 UTC (GMT)
1000 0000 1000 0000 1000 0000 1000 0000 1000 0000 1000 0000 1000 0000 1000 1110 = 9,259,542,123,273,814,158 Sep 28 09:33 UTC (GMT)
11 1111 0001 0011 = 16,147 Sep 28 09:33 UTC (GMT)
11 1110 1010 1101 0111 = 256,727 Sep 28 09:33 UTC (GMT)
1111 1111 1111 1111 1111 1111 1111 0011 0000 0000 0000 0000 0000 0000 0001 1111 = 18,446,744,017,874,976,799 Sep 28 09:32 UTC (GMT)
1 1001 1101 1011 = 6,619 Sep 28 09:31 UTC (GMT)
1011 0111 0001 1111 1100 0110 0000 0000 0000 0011 1111 1111 1111 1000 0001 1111 = 13,195,483,136,588,249,119 Sep 28 09:30 UTC (GMT)
10 0011 1110 1010 = 9,194 Sep 28 09:30 UTC (GMT)
1011 1001 0100 1111 1111 1111 1111 1001 = 3,109,027,833 Sep 28 09:29 UTC (GMT)
1010 0110 0111 1100 = 42,620 Sep 28 09:29 UTC (GMT)
1111 1111 1111 1111 1111 1111 0111 0101 = 4,294,967,157 Sep 28 09:28 UTC (GMT)
1110 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0001 = 16,140,901,064,495,857,665 Sep 28 09:26 UTC (GMT)
All the converted unsigned binary numbers, from base two to base ten

How to convert unsigned binary numbers from binary system to decimal? Simply convert from base two to base ten.

To understand how to convert a number from base two to base ten, the easiest way is to do it through an example - convert the number from base two, 101 0011(2), to base ten:

  • Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresponding power of 2 by exactly one unit each time we move to the left:
  • powers of 2: 6 5 4 3 2 1 0
    digits: 1 0 1 0 0 1 1
  • Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up:

    101 0011(2) =


    (1 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =


    (64 + 0 + 16 + 0 + 0 + 2 + 1)(10) =


    (64 + 16 + 2 + 1)(10) =


    83(10)

  • Binary unsigned number (base 2), 101 0011(2) = 83(10), unsigned positive integer in base 10