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

Unsigned binary (base 2) 10(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:

    • 21

      1
    • 20

      0

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

10(2) =


(1 × 21 + 0 × 20)(10) =


(2 + 0)(10) =


2(10)

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


More operations of this kind:

01 = ?

11 = ?


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 = 2 Mar 02 14:09 UTC (GMT)
10 0001 0000 0000 0000 0000 1111 0000 0000 0000 0000 0001 1110 0001 1110 1000 = 2,377,901,634,043,896,296 Mar 02 14:08 UTC (GMT)
10 1010 0011 1000 0011 0111 = 2,766,903 Mar 02 14:07 UTC (GMT)
1 0000 0000 0000 0100 0000 1001 = 16,778,249 Mar 02 14:07 UTC (GMT)
11 1010 0101 = 933 Mar 02 14:07 UTC (GMT)
110 0111 0011 = 1,651 Mar 02 14:07 UTC (GMT)
1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1000 = 1,152,921,504,606,846,984 Mar 02 14:07 UTC (GMT)
1000 1110 1101 1110 1101 1110 1100 1000 0100 0000 1101 1000 1101 1100 = 40,214,495,116,712,156 Mar 02 14:06 UTC (GMT)
111 1010 0000 1010 = 31,242 Mar 02 14:06 UTC (GMT)
1 1001 1110 1000 1011 1001 0101 1100 = 434,682,204 Mar 02 14:06 UTC (GMT)
1 1111 = 31 Mar 02 14:06 UTC (GMT)
1010 1101 0010 0100 = 44,324 Mar 02 14:05 UTC (GMT)
1100 1111 0101 = 3,317 Mar 02 14:05 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