Unsigned binary number (base two) 10 1010 1010 0101 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
10 1010 1010 0101(2)
to a positive integer (no sign) in decimal system (in base 10)

1. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

    • 213

      1
    • 212

      0
    • 211

      1
    • 210

      0
    • 29

      1
    • 28

      0
    • 27

      1
    • 26

      0
    • 25

      1
    • 24

      0
    • 23

      0
    • 22

      1
    • 21

      0
    • 20

      1

2. Multiply each bit by its corresponding power of 2 and add all the terms up:

10 1010 1010 0101(2) =


(1 × 213 + 0 × 212 + 1 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =


(8 192 + 0 + 2 048 + 0 + 512 + 0 + 128 + 0 + 32 + 0 + 0 + 4 + 0 + 1)(10) =


(8 192 + 2 048 + 512 + 128 + 32 + 4 + 1)(10) =


10 917(10)

Conclusion:

Number 10 1010 1010 0101(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


10 1010 1010 0101(2) = 10 917(10)

Spaces used to group digits: for binary, by 4; for decimal, by 3.


More operations of this kind:

10 1010 1010 0100 = ?

10 1010 1010 0110 = ?


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 0101 = 10,917 Jan 26 18:27 UTC (GMT)
110 0000 = 96 Jan 26 18:27 UTC (GMT)
10 1100 0111 = 711 Jan 26 18:26 UTC (GMT)
1001 0101 1100 0111 = 38,343 Jan 26 18:25 UTC (GMT)
10 0010 0110 0000 0000 0000 0000 0110 = 576,716,806 Jan 26 18:24 UTC (GMT)
1001 0001 0000 0010 = 37,122 Jan 26 18:24 UTC (GMT)
111 1000 0000 0001 = 30,721 Jan 26 18:23 UTC (GMT)
1000 1000 1011 0110 = 34,998 Jan 26 18:23 UTC (GMT)
110 0111 = 103 Jan 26 18:23 UTC (GMT)
101 1000 1100 1010 1100 = 363,692 Jan 26 18:22 UTC (GMT)
1101 1011 1100 0011 = 56,259 Jan 26 18:22 UTC (GMT)
1110 0100 1010 1000 1001 0100 1010 0101 0011 0001 1001 0100 0111 = 4,022,603,191,884,103 Jan 26 18:21 UTC (GMT)
1100 0111 1001 1001 = 51,097 Jan 26 18:21 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