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)

10 1010 1010 = 682 Apr 04 18:09 UTC (GMT)
10 0001 0000 1000 0000 0010 0000 = 34,635,808 Apr 04 18:09 UTC (GMT)
10 0011 = 35 Apr 04 18:08 UTC (GMT)
111 1000 0010 1010 1010 = 492,202 Apr 04 18:08 UTC (GMT)
1111 0000 1111 0000 1111 = 986,895 Apr 04 18:05 UTC (GMT)
1 0111 = 23 Apr 04 18:05 UTC (GMT)
1110 0111 = 231 Apr 04 18:04 UTC (GMT)
1101 1011 = 219 Apr 04 18:03 UTC (GMT)
1001 1001 0100 1001 = 39,241 Apr 04 18:02 UTC (GMT)
1000 1100 0100 0110 = 35,910 Apr 04 18:02 UTC (GMT)
1101 1010 = 218 Apr 04 18:00 UTC (GMT)
10 0100 = 36 Apr 04 17:56 UTC (GMT)
1 1110 0110 0001 = 7,777 Apr 04 17:54 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