Unsigned binary number (base two) 1000 0000 0000 1111 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1000 0000 0000 1111(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:

    • 215

      1
    • 214

      0
    • 213

      0
    • 212

      0
    • 211

      0
    • 210

      0
    • 29

      0
    • 28

      0
    • 27

      0
    • 26

      0
    • 25

      0
    • 24

      0
    • 23

      1
    • 22

      1
    • 21

      1
    • 20

      1

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

1000 0000 0000 1111(2) =


(1 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =


(32 768 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 + 4 + 2 + 1)(10) =


(32 768 + 8 + 4 + 2 + 1)(10) =


32 783(10)

Conclusion:

Number 1000 0000 0000 1111(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1000 0000 0000 1111(2) = 32 783(10)

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


More operations of this kind:

1000 0000 0000 1110 = ?

1000 0000 0001 0000 = ?


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 0000 0000 1111 = 32,783 Nov 26 23:37 UTC (GMT)
1101 1101 1111 0101 = 56,821 Nov 26 23:36 UTC (GMT)
111 1100 1011 0000 = 31,920 Nov 26 23:36 UTC (GMT)
1101 1011 = 219 Nov 26 23:36 UTC (GMT)
101 1110 1101 = 1,517 Nov 26 23:35 UTC (GMT)
1101 1101 1101 1101 1101 1100 = 14,540,252 Nov 26 23:35 UTC (GMT)
11 1001 1100 = 924 Nov 26 23:35 UTC (GMT)
1111 1110 = 254 Nov 26 23:35 UTC (GMT)
100 0111 0110 1111 1100 = 292,604 Nov 26 23:34 UTC (GMT)
1110 0010 = 226 Nov 26 23:34 UTC (GMT)
100 1100 = 76 Nov 26 23:34 UTC (GMT)
1 0000 1000 0000 0010 0000 = 1,081,376 Nov 26 23:33 UTC (GMT)
111 1111 1111 0011 = 32,755 Nov 26 23:33 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