Unsigned binary number (base two) 1 1101 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1 1101(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:

    • 24

      1
    • 23

      1
    • 22

      1
    • 21

      0
    • 20

      1

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

1 1101(2) =


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


(16 + 8 + 4 + 0 + 1)(10) =


(16 + 8 + 4 + 1)(10) =


29(10)

Conclusion:

Number 1 1101(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1 1101(2) = 29(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 1101 = 29 Apr 18 22:21 UTC (GMT)
1100 1111 1100 0111 = 53,191 Apr 18 22:21 UTC (GMT)
10 0010 0001 0010 = 8,722 Apr 18 22:13 UTC (GMT)
110 1110 1101 1010 0011 = 454,051 Apr 18 22:12 UTC (GMT)
1010 0000 0110 1001 = 41,065 Apr 18 22:07 UTC (GMT)
1 1000 1100 1001 1000 = 101,528 Apr 18 22:03 UTC (GMT)
1111 1111 1001 0100 = 65,428 Apr 18 22:02 UTC (GMT)
101 0000 0111 = 1,287 Apr 18 22:01 UTC (GMT)
1 0001 1000 1101 = 4,493 Apr 18 21:58 UTC (GMT)
1111 0000 1111 = 3,855 Apr 18 21:47 UTC (GMT)
1 1001 1010 = 410 Apr 18 21:34 UTC (GMT)
1 0101 1111 0101 = 5,621 Apr 18 21:29 UTC (GMT)
101 0000 = 80 Apr 18 21:22 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