Unsigned binary number (base two) 10 1001 1010 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
10 1001 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:

    • 29

      1
    • 28

      0
    • 27

      1
    • 26

      0
    • 25

      0
    • 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:

10 1001 1010(2) =


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


(512 + 0 + 128 + 0 + 0 + 16 + 8 + 0 + 2 + 0)(10) =


(512 + 128 + 16 + 8 + 2)(10) =


666(10)

Conclusion:

Number 10 1001 1010(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


10 1001 1010(2) = 666(10)

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


More operations of this kind:

10 1001 1001 = ?

10 1001 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)

10 1001 1010 = 666 Jan 20 12:52 UTC (GMT)
1000 0011 0010 1010 = 33,578 Jan 20 12:51 UTC (GMT)
111 0000 1111 0001 1110 0111 1000 1110 1111 = 30,318,426,351 Jan 20 12:51 UTC (GMT)
11 1110 0001 1111 1111 1111 1111 1110 = 1,042,284,542 Jan 20 12:51 UTC (GMT)
1100 0000 0000 0110 = 49,158 Jan 20 12:51 UTC (GMT)
100 1101 0100 1100 = 19,788 Jan 20 12:49 UTC (GMT)
101 1010 1101 0111 = 23,255 Jan 20 12:49 UTC (GMT)
1000 0010 0100 0101 1100 0001 0100 0010 = 2,185,609,538 Jan 20 12:47 UTC (GMT)
1111 0110 0101 1100 = 63,068 Jan 20 12:47 UTC (GMT)
11 1111 = 63 Jan 20 12:47 UTC (GMT)
1 0010 = 18 Jan 20 12:46 UTC (GMT)
1101 1000 1000 0010 = 55,426 Jan 20 12:45 UTC (GMT)
1 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 = 562,949,953,421,311 Jan 20 12:45 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