Unsigned binary number (base two) 10 1001 1111 converted to decimal system (base ten) positive integer

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

    • 29

      1
    • 28

      0
    • 27

      1
    • 26

      0
    • 25

      0
    • 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:

10 1001 1111(2) =


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


(512 + 0 + 128 + 0 + 0 + 16 + 8 + 4 + 2 + 1)(10) =


(512 + 128 + 16 + 8 + 4 + 2 + 1)(10) =


671(10)

Conclusion:

Number 10 1001 1111(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


10 1001 1111(2) = 671(10)

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

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 1111 = 671 Jun 19 19:30 UTC (GMT)
1011 1001 0011 = 2,963 Jun 19 19:30 UTC (GMT)
1 1101 0100 = 468 Jun 19 19:29 UTC (GMT)
1 0000 0001 = 257 Jun 19 19:28 UTC (GMT)
11 1010 = 58 Jun 19 19:24 UTC (GMT)
1101 1000 1000 0010 = 55,426 Jun 19 19:22 UTC (GMT)
110 1001 1011 = 1,691 Jun 19 19:21 UTC (GMT)
111 1101 1101 = 2,013 Jun 19 19:15 UTC (GMT)
1 1111 1000 = 504 Jun 19 19:15 UTC (GMT)
1001 1101 0011 0000 = 40,240 Jun 19 19:14 UTC (GMT)
11 1111 1100 = 1,020 Jun 19 19:13 UTC (GMT)
100 1010 1011 1010 1000 = 306,088 Jun 19 19:12 UTC (GMT)
100 0001 0001 = 1,041 Jun 19 19:08 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