Unsigned binary number (base two) 1 0010 1001 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1 0010 1001(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:

    • 28

      1
    • 27

      0
    • 26

      0
    • 25

      1
    • 24

      0
    • 23

      1
    • 22

      0
    • 21

      0
    • 20

      1

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

1 0010 1001(2) =


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


(256 + 0 + 0 + 32 + 0 + 8 + 0 + 0 + 1)(10) =


(256 + 32 + 8 + 1)(10) =


297(10)

Conclusion:

Number 1 0010 1001(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1 0010 1001(2) = 297(10)

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


More operations of this kind:

1 0010 1000 = ?

1 0010 1010 = ?


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 0010 1001 = 297 Nov 26 23:03 UTC (GMT)
100 1001 0010 1001 = 18,729 Nov 26 23:03 UTC (GMT)
11 0100 1100 = 844 Nov 26 23:02 UTC (GMT)
100 1001 0010 1000 = 18,728 Nov 26 23:01 UTC (GMT)
100 1001 0010 1000 = 18,728 Nov 26 23:01 UTC (GMT)
10 0110 1010 = 618 Nov 26 23:01 UTC (GMT)
1 1100 1000 = 456 Nov 26 23:01 UTC (GMT)
1 0001 1001 = 281 Nov 26 23:01 UTC (GMT)
1110 = 14 Nov 26 23:00 UTC (GMT)
101 1010 1101 0111 = 23,255 Nov 26 23:00 UTC (GMT)
1111 0000 = 240 Nov 26 23:00 UTC (GMT)
1111 0110 0101 0000 = 63,056 Nov 26 22:59 UTC (GMT)
100 1001 0010 1000 = 18,728 Nov 26 22:58 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