Converter from binary one's complement: converting to decimal system (base ten) integer numbers

Convert numbers from binary one's complement to decimal system (base ten) integers

Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - or else extra bits of '0' value will be added in front (to the left).

Latest binary numbers in one's complement representation converted to signed integers numbers in decimal system (base ten)

1010 1011 = -84Mar 29 12:41 UTC (GMT)
0111 1011 = 123Mar 29 12:40 UTC (GMT)
1111 1000 = -7Mar 29 12:36 UTC (GMT)
1111 1110 1101 0101 = -298Mar 29 12:35 UTC (GMT)
1000 0000 0000 0000 1000 1000 1011 1000 = -2,147,448,647Mar 29 12:35 UTC (GMT)
0000 0001 1010 1010 = 426Mar 29 12:35 UTC (GMT)
0000 0001 0011 0011 = 307Mar 29 12:20 UTC (GMT)
0101 0101 1011 1010 = 21,946Mar 29 12:01 UTC (GMT)
1010 0111 = -88Mar 29 11:59 UTC (GMT)
1101 1111 = -32Mar 29 11:58 UTC (GMT)
0101 0010 = 82Mar 29 11:57 UTC (GMT)
0000 0000 0000 0000 1010 1001 1001 1011 1000 1101 1000 1100 1001 0001 1001 0010 = 186,485,559,824,786Mar 29 11:54 UTC (GMT)
0000 1001 = 9Mar 29 11:54 UTC (GMT)

How to convert binary numbers in one's complement representation from binary system to decimal

To understand how to convert a binary number in one's complement representation from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1101, to base ten:

  • In a binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so the number is negative.
  • Get the binary representation of the positive number, flip all the bits in the binary one's complement representation - replace the bits set on 1 with 0-s and the bits set on 0 with 1-s:
    !(1001 1101) = 0110 0010
  • Write bellow the positive binary number representation in base two, and above each bit that makes up the binary number write the corresponding powers of 2 (numeral base), starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresonding power of 2 with exactly one unit:
  • powers of 2 7 6 5 4 3 2 1 0
    number's digits 0 1 1 0 0 0 1 0
  • 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 summing up all the terms:
    0110 0010(2) =
    = 0 * 27 + 1 * 26 + 1 * 25 + 0 * 24 + 0 * 23 + 0 * 22 + 1 * 21 + 0 * 20 =
    = 0 + 64 + 32 + 0 + 0 + 0 + 2 + 0 =
    = 64 + 32 + 2 =
    = 98(10)
  • Binary one's complement number, 1001 1110 = -98(10), signed negative integer in base 10