Unsigned binary number (base two) 101 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
101(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:

    • 22

      1
    • 21

      0
    • 20

      1

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

101(2) =


(1 × 22 + 0 × 21 + 1 × 20)(10) =


(4 + 0 + 1)(10) =


(4 + 1)(10) =


5(10)

Conclusion:

Number 101(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


101(2) = 5(10)

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)

101 = 5 Apr 20 19:08 UTC (GMT)
1011 1111 0010 0110 0110 0110 0110 0110 = 3,206,964,838 Apr 20 19:01 UTC (GMT)
100 1011 = 75 Apr 20 19:00 UTC (GMT)
10 1011 1100 = 700 Apr 20 18:55 UTC (GMT)
10 1001 1010 = 666 Apr 20 18:53 UTC (GMT)
1011 0101 0100 = 2,900 Apr 20 18:52 UTC (GMT)
11 1111 1000 0000 = 16,256 Apr 20 18:49 UTC (GMT)
110 0100 = 100 Apr 20 18:48 UTC (GMT)
111 1111 0000 = 2,032 Apr 20 18:48 UTC (GMT)
1 0001 1000 = 280 Apr 20 18:46 UTC (GMT)
1100 0011 1010 1000 0000 0000 0000 0000 = 3,282,567,168 Apr 20 18:46 UTC (GMT)
11 1100 = 60 Apr 20 18:46 UTC (GMT)
1100 1111 0000 0000 0000 0000 = 13,565,952 Apr 20 18:45 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