Unsigned binary number (base two) 1 1111 1111 1111 1111 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1 1111 1111 1111 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:

    • 216

      1
    • 215

      1
    • 214

      1
    • 213

      1
    • 212

      1
    • 211

      1
    • 210

      1
    • 29

      1
    • 28

      1
    • 27

      1
    • 26

      1
    • 25

      1
    • 24

      1
    • 23

      1
    • 22

      1
    • 21

      1
    • 20

      1

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

1 1111 1111 1111 1111(2) =


(1 × 216 + 1 × 215 + 1 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =


(65 536 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =


131 071(10)

Conclusion:

Number 1 1111 1111 1111 1111(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1 1111 1111 1111 1111(2) = 131 071(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)

1 1111 1111 1111 1111 = 131,071 Apr 18 14:19 UTC (GMT)
1 0010 1001 = 297 Apr 18 14:15 UTC (GMT)
11 1110 = 62 Apr 18 14:13 UTC (GMT)
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 = 4,503,599,627,370,495 Apr 18 14:08 UTC (GMT)
1011 1011 = 187 Apr 18 14:06 UTC (GMT)
1 1001 = 25 Apr 18 13:59 UTC (GMT)
1111 0100 0010 1100 = 62,508 Apr 18 13:59 UTC (GMT)
111 0111 = 119 Apr 18 13:58 UTC (GMT)
1100 0101 0110 1001 0111 1011 = 12,937,595 Apr 18 13:58 UTC (GMT)
111 1101 1110 = 2,014 Apr 18 13:57 UTC (GMT)
10 1001 = 41 Apr 18 13:56 UTC (GMT)
10 0010 0111 = 551 Apr 18 13:56 UTC (GMT)
1010 1011 = 171 Apr 18 13:55 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