Unsigned binary number (base two) 110 1000 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
110 1000(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:

    • 26

      1
    • 25

      1
    • 24

      0
    • 23

      1
    • 22

      0
    • 21

      0
    • 20

      0

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

110 1000(2) =


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


(64 + 32 + 0 + 8 + 0 + 0 + 0)(10) =


(64 + 32 + 8)(10) =


104(10)

Conclusion:

Number 110 1000(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


110 1000(2) = 104(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)

110 1000 = 104 Feb 28 00:09 UTC (GMT)
1 0001 0001 0001 0001 0001 0001 0001 = 286,331,153 Feb 28 00:08 UTC (GMT)
100 0101 1001 = 1,113 Feb 28 00:05 UTC (GMT)
110 1100 1001 = 1,737 Feb 28 00:05 UTC (GMT)
1100 1001 = 201 Feb 28 00:04 UTC (GMT)
1111 0001 = 241 Feb 28 00:04 UTC (GMT)
1100 0111 = 199 Feb 28 00:04 UTC (GMT)
101 1011 = 91 Feb 28 00:03 UTC (GMT)
101 0000 = 80 Feb 28 00:03 UTC (GMT)
1001 1101 = 157 Feb 28 00:00 UTC (GMT)
1001 0000 = 144 Feb 28 00:00 UTC (GMT)
110 1010 = 106 Feb 27 23:59 UTC (GMT)
11 1001 = 57 Feb 27 23:59 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