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)

1001 1010 = -101May 28 23:58 UTC (GMT)
1010 1111 = -80May 28 23:34 UTC (GMT)
0001 1010 = 26May 28 23:33 UTC (GMT)
0000 1000 = 8May 28 23:28 UTC (GMT)
1110 0101 = -26May 28 23:27 UTC (GMT)
0011 = 3May 28 23:17 UTC (GMT)
0011 0110 = 54May 28 23:17 UTC (GMT)
0011 1010 = 58May 28 23:16 UTC (GMT)
0011 1111 1111 1111 1111 1111 0110 1011 = 1,073,741,675May 28 22:58 UTC (GMT)
1110 1010 = -21May 28 22:56 UTC (GMT)
1101 0011 = -44May 28 22:53 UTC (GMT)
1010 1010 1011 1110 = -21,825May 28 22:37 UTC (GMT)
0000 0001 0001 1001 = 281May 28 22:37 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