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)

1100 0111 = 199 Sep 23 10:46 UTC (GMT)
110 0101 0010 = 1,618 Sep 23 10:45 UTC (GMT)
1101 1101 = 221 Sep 23 10:43 UTC (GMT)
11 1101 = 61 Sep 23 10:20 UTC (GMT)
1010 0100 = 164 Sep 23 10:20 UTC (GMT)
11 1000 1011 = 907 Sep 23 10:15 UTC (GMT)
111 1111 1000 = 2,040 Sep 23 10:12 UTC (GMT)
1100 1111 0000 0000 0000 0000 = 13,565,952 Sep 23 10:06 UTC (GMT)
1100 1111 0000 0000 0000 0000 = 13,565,952 Sep 23 10:06 UTC (GMT)
1100 0010 = 194 Sep 23 10:01 UTC (GMT)
11 1100 0000 = 960 Sep 23 09:51 UTC (GMT)
1101 0011 0001 1111 = 54,047 Sep 23 09:45 UTC (GMT)
1100 0000 = 192 Sep 23 09:44 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