Unsigned binary number (base two) 1101 0000 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1101 0000(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:

    • 27

      1
    • 26

      1
    • 25

      0
    • 24

      1
    • 23

      0
    • 22

      0
    • 21

      0
    • 20

      0

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

1101 0000(2) =


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


(128 + 64 + 0 + 16 + 0 + 0 + 0 + 0)(10) =


(128 + 64 + 16)(10) =


208(10)

Conclusion:

Number 1101 0000(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1101 0000(2) = 208(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)

1101 0000 = 208 Dec 12 00:36 UTC (GMT)
1010 1100 = 172 Dec 12 00:29 UTC (GMT)
101 1101 0011 0000 0000 0000 = 6,107,136 Dec 12 00:27 UTC (GMT)
111 1110 0001 = 2,017 Dec 12 00:27 UTC (GMT)
111 0000 1111 1001 1001 1100 1000 = 118,462,920 Dec 12 00:26 UTC (GMT)
1111 1000 0101 0011 = 63,571 Dec 12 00:26 UTC (GMT)
10 1011 1110 = 702 Dec 12 00:25 UTC (GMT)
111 0001 = 113 Dec 12 00:24 UTC (GMT)
1001 1100 0011 1100 = 39,996 Dec 12 00:23 UTC (GMT)
101 1010 0010 = 1,442 Dec 12 00:22 UTC (GMT)
1000 1111 = 143 Dec 12 00:17 UTC (GMT)
10 1000 = 40 Dec 12 00:15 UTC (GMT)
110 0000 0000 = 1,536 Dec 12 00:15 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