Unsigned binary number (base two) 1010 converted to decimal system (base ten) positive integer

Unsigned binary (base 2) 1010(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:

    • 23

      1
    • 22

      0
    • 21

      1
    • 20

      0

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

1010(2) =


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


(8 + 0 + 2 + 0)(10) =


(8 + 2)(10) =


10(10)

Number 1010(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):
1010(2) = 10(10)


More operations of this kind:

1001 = ?

1011 = ?


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)

1010 = 10 Jun 14 00:06 UTC (GMT)
1001 1010 0100 0111 = 39,495 Jun 14 00:05 UTC (GMT)
110 0101 0111 1000 1100 0010 = 6,650,050 Jun 14 00:05 UTC (GMT)
1000 1011 0100 0101 = 35,653 Jun 14 00:05 UTC (GMT)
11 1010 0111 1010 0110 0011 0110 0000 = 981,099,360 Jun 14 00:05 UTC (GMT)
1 0100 0100 1001 = 5,193 Jun 14 00:05 UTC (GMT)
1010 0100 0000 1001 = 41,993 Jun 14 00:04 UTC (GMT)
10 0101 0011 1100 = 9,532 Jun 14 00:04 UTC (GMT)
1101 1011 1011 1110 = 56,254 Jun 14 00:04 UTC (GMT)
11 0101 0101 0100 0000 0101 0110 1010 1010 = 14,315,181,738 Jun 14 00:04 UTC (GMT)
1001 0000 0101 1111 0000 0001 0000 0000 0001 0111 0010 1110 1010 1011 1010 1001 = 10,403,034,764,149,697,449 Jun 14 00:03 UTC (GMT)
100 1111 1011 1010 = 20,410 Jun 14 00:03 UTC (GMT)
100 1000 1011 = 1,163 Jun 14 00:03 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