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 0001 0100 0010 0001 0100 0000 0011 = 3,242,333,187 Dec 03 00:56 UTC (GMT)
100 1011 0010 1001 0101 0001 0101 0010 1010 0010 0101 0101 0101 0100 1001 0100 = 5,415,949,442,242,401,428 Dec 03 00:56 UTC (GMT)
1010 0110 0010 1110 0000 1110 1000 0110 1100 1110 0000 0100 1010 0110 1100 1111 = 11,974,524,431,369,545,423 Dec 03 00:56 UTC (GMT)
1 0010 1011 0101 = 4,789 Dec 03 00:54 UTC (GMT)
101 0101 0101 1001 = 21,849 Dec 03 00:52 UTC (GMT)
1111 0001 1011 1011 = 61,883 Dec 03 00:52 UTC (GMT)
10 1111 = 47 Dec 03 00:51 UTC (GMT)
1001 0111 1001 1111 = 38,815 Dec 03 00:50 UTC (GMT)
111 0101 1010 1010 1101 1110 1111 1011 = 1,974,132,475 Dec 03 00:50 UTC (GMT)
11 1111 = 63 Dec 03 00:48 UTC (GMT)
1111 1111 1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 18,442,240,474,082,181,120 Dec 03 00:48 UTC (GMT)
1001 1010 1011 1110 = 39,614 Dec 03 00:48 UTC (GMT)
111 1010 = 122 Dec 03 00:47 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