Unsigned binary number (base two) 100 1100 converted to decimal system (base ten) positive integer

Unsigned binary (base 2) 100 1100(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

      0
    • 24

      0
    • 23

      1
    • 22

      1
    • 21

      0
    • 20

      0

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

100 1100(2) =


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


(64 + 0 + 0 + 8 + 4 + 0 + 0)(10) =


(64 + 8 + 4)(10) =


76(10)

Number 100 1100(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):
100 1100(2) = 76(10)

Spaces used to group digits: for binary, by 4.


More operations of this kind:

100 1011 = ?

100 1101 = ?


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)

100 1100 = 76 Oct 28 10:54 UTC (GMT)
100 0010 1111 0110 0100 0000 0000 0111 = 1,123,434,503 Oct 28 10:54 UTC (GMT)
1100 1100 1110 0111 0011 = 839,283 Oct 28 10:54 UTC (GMT)
101 0001 = 81 Oct 28 10:54 UTC (GMT)
111 1001 0011 0100 1101 1010 0010 0110 = 2,033,506,854 Oct 28 10:53 UTC (GMT)
1001 1111 1111 1111 1111 1111 1111 1111 = 2,684,354,559 Oct 28 10:53 UTC (GMT)
1 0001 0010 = 274 Oct 28 10:53 UTC (GMT)
10 0000 0111 0100 0000 0000 0000 0111 = 544,473,095 Oct 28 10:52 UTC (GMT)
10 0010 1101 1101 = 8,925 Oct 28 10:52 UTC (GMT)
1 0000 0000 0000 0000 0000 0000 0001 0110 = 4,294,967,318 Oct 28 10:52 UTC (GMT)
101 1111 0000 0000 = 24,320 Oct 28 10:51 UTC (GMT)
1 0000 0000 0000 0100 0000 1011 = 16,778,251 Oct 28 10:51 UTC (GMT)
101 1110 1010 0000 0011 = 387,587 Oct 28 10:51 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