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)

111 0001 = 113 Sep 25 01:05 UTC (GMT)
10 0000 0000 = 512 Sep 25 01:04 UTC (GMT)
1100 1010 = 202 Sep 25 00:57 UTC (GMT)
11 0110 0111 = 871 Sep 25 00:52 UTC (GMT)
11 1100 1000 1101 = 15,501 Sep 25 00:51 UTC (GMT)
1111 1000 = 248 Sep 25 00:46 UTC (GMT)
1101 1101 = 221 Sep 25 00:45 UTC (GMT)
110 1000 = 104 Sep 25 00:43 UTC (GMT)
1000 1101 0000 1000 0000 0000 0100 0000 = 2,366,111,808 Sep 25 00:34 UTC (GMT)
101 1010 = 90 Sep 25 00:33 UTC (GMT)
1101 1001 = 217 Sep 25 00:25 UTC (GMT)
111 1011 = 123 Sep 25 00:23 UTC (GMT)
10 0101 1101 0011 0000 0000 0000 = 39,661,568 Sep 25 00:22 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