Unsigned binary number (base two) 100 1011 1010 converted to decimal system (base ten) positive integer

Unsigned binary (base 2) 100 1011 1010(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:

    • 210

      1
    • 29

      0
    • 28

      0
    • 27

      1
    • 26

      0
    • 25

      1
    • 24

      1
    • 23

      1
    • 22

      0
    • 21

      1
    • 20

      0

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

100 1011 1010(2) =


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


(1 024 + 0 + 0 + 128 + 0 + 32 + 16 + 8 + 0 + 2 + 0)(10) =


(1 024 + 128 + 32 + 16 + 8 + 2)(10) =


1 210(10)

Number 100 1011 1010(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):
100 1011 1010(2) = 1 210(10)

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


More operations of this kind:

100 1011 1001 = ?

100 1011 1011 = ?


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)

100 1011 1010 = 1,210 Sep 28 08:45 UTC (GMT)
111 1011 1101 0000 = 31,696 Sep 28 08:45 UTC (GMT)
1011 0010 = 178 Sep 28 08:45 UTC (GMT)
100 0001 0101 0010 0000 0000 0000 0101 = 1,095,892,997 Sep 28 08:44 UTC (GMT)
111 1010 0001 0010 1010 = 500,010 Sep 28 08:44 UTC (GMT)
11 1101 1101 0101 1111 1001 0000 0000 = 1,037,433,088 Sep 28 08:43 UTC (GMT)
1 1011 1111 1110 = 7,166 Sep 28 08:42 UTC (GMT)
1 0110 1110 0001 = 5,857 Sep 28 08:41 UTC (GMT)
11 1111 1001 = 1,017 Sep 28 08:41 UTC (GMT)
100 0111 1100 = 1,148 Sep 28 08:40 UTC (GMT)
1101 1000 1110 = 3,470 Sep 28 08:39 UTC (GMT)
1101 1111 1010 1010 = 57,258 Sep 28 08:38 UTC (GMT)
10 1101 1100 1110 = 11,726 Sep 28 08:38 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