Unsigned binary number (base two) 1 0101 1001 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1 0101 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

      1
    • 25

      0
    • 24

      1
    • 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 0101 1001(2) =


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


(256 + 0 + 64 + 0 + 16 + 8 + 0 + 0 + 1)(10) =


(256 + 64 + 16 + 8 + 1)(10) =


345(10)

Conclusion:

Number 1 0101 1001(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1 0101 1001(2) = 345(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)

1 0101 1001 = 345 Aug 18 07:17 UTC (GMT)
1 1011 0100 1001 = 6,985 Aug 18 07:17 UTC (GMT)
10 0111 1000 0111 0001 = 161,905 Aug 18 07:16 UTC (GMT)
1100 0001 = 193 Aug 18 07:13 UTC (GMT)
1101 0001 0100 1011 = 53,579 Aug 18 07:12 UTC (GMT)
1111 0011 1100 0100 = 62,404 Aug 18 07:09 UTC (GMT)
101 1110 = 94 Aug 18 07:09 UTC (GMT)
1 0000 0000 = 256 Aug 18 07:07 UTC (GMT)
1011 = 11 Aug 18 07:06 UTC (GMT)
1000 0111 1101 = 2,173 Aug 18 07:05 UTC (GMT)
1111 1000 = 248 Aug 18 07:04 UTC (GMT)
1011 0101 1011 1011 = 46,523 Aug 18 07:01 UTC (GMT)
10 1100 0101 = 709 Aug 18 06:59 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