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 0100 1110 1000 = 13,544 Apr 14 10:55 UTC (GMT)
1 1010 1011 1110 0000 1001 0010 1000 = 448,661,800 Apr 14 10:55 UTC (GMT)
100 0011 1011 1110 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 = 4,881,550,152,348,729,346 Apr 14 10:55 UTC (GMT)
100 0011 1011 1110 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 4,881,550,152,348,729,344 Apr 14 10:55 UTC (GMT)
101 1010 0100 0011 = 23,107 Apr 14 10:55 UTC (GMT)
110 0101 0110 0100 = 25,956 Apr 14 10:55 UTC (GMT)
10 1010 1000 0111 0111 1111 1111 0001 = 713,523,185 Apr 14 10:55 UTC (GMT)
1110 0001 0000 0100 0010 = 921,666 Apr 14 10:54 UTC (GMT)
1010 1010 0101 0000 = 43,600 Apr 14 10:53 UTC (GMT)
100 0010 1110 0100 0111 1111 1111 1111 = 1,122,271,231 Apr 14 10:53 UTC (GMT)
1101 0111 0011 = 3,443 Apr 14 10:53 UTC (GMT)
1000 0000 0000 0000 0000 0000 0010 0101 = 2,147,483,685 Apr 14 10:53 UTC (GMT)
11 0111 1011 0011 1110 0111 1011 0101 0001 = 14,952,594,257 Apr 14 10:53 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