Unsigned binary number (base two) 10 1000 converted to decimal system (base ten) positive integer

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

    • 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:

10 1000(2) =


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


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


(32 + 8)(10) =


40(10)

Conclusion:

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


10 1000(2) = 40(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 1000 = 40 Sep 18 07:57 UTC (GMT)
1100 0001 = 193 Sep 18 07:56 UTC (GMT)
1010 1111 = 175 Sep 18 07:55 UTC (GMT)
1100 0000 0000 0000 0000 0000 0000 = 201,326,592 Sep 18 07:54 UTC (GMT)
10 1011 1100 = 700 Sep 18 07:53 UTC (GMT)
10 0000 0000 0000 = 8,192 Sep 18 07:51 UTC (GMT)
110 1000 = 104 Sep 18 07:50 UTC (GMT)
1001 1010 = 154 Sep 18 07:49 UTC (GMT)
1001 1010 = 154 Sep 18 07:49 UTC (GMT)
10 1000 = 40 Sep 18 07:49 UTC (GMT)
100 0111 1100 = 1,148 Sep 18 07:48 UTC (GMT)
101 0000 = 80 Sep 18 07:47 UTC (GMT)
1111 1100 = 252 Sep 18 07:45 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