Unsigned binary number (base two) 1000 1010 0000 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1000 1010 0000(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:

    • 211

      1
    • 210

      0
    • 29

      0
    • 28

      0
    • 27

      1
    • 26

      0
    • 25

      1
    • 24

      0
    • 23

      0
    • 22

      0
    • 21

      0
    • 20

      0

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

1000 1010 0000(2) =


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


(2 048 + 0 + 0 + 0 + 128 + 0 + 32 + 0 + 0 + 0 + 0 + 0)(10) =


(2 048 + 128 + 32)(10) =


2 208(10)

Conclusion:

Number 1000 1010 0000(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1000 1010 0000(2) = 2 208(10)

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

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)

1000 1010 0000 = 2,208 May 20 16:31 UTC (GMT)
110 0111 = 103 May 20 16:29 UTC (GMT)
100 1010 0001 = 1,185 May 20 16:28 UTC (GMT)
1010 1001 = 169 May 20 16:27 UTC (GMT)
1010 1001 = 169 May 20 16:27 UTC (GMT)
10 1010 1010 = 682 May 20 16:27 UTC (GMT)
1010 1001 = 169 May 20 16:27 UTC (GMT)
1111 1111 = 255 May 20 16:26 UTC (GMT)
1000 0000 0100 = 2,052 May 20 16:26 UTC (GMT)
1001 0100 1111 1111 = 38,143 May 20 16:26 UTC (GMT)
1 1101 = 29 May 20 16:25 UTC (GMT)
1 0111 1111 1011 = 6,139 May 20 16:24 UTC (GMT)
100 0010 = 66 May 20 16:23 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