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

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

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

How to convert a signed binary number in one's complement representation to an integer in base ten:

1) In a signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive.

2) Construct the unsigned binary number: flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s.

3) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

4) Add all the terms up to get the positive integer number in base ten.

5) Adjust the sign of the integer number by the first bit of the initial binary number.

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

1100 1111 1110 0000 = -12,319 Jun 26 19:55 UTC (GMT)
1101 0011 1110 1010 = -11,285 Jun 26 19:54 UTC (GMT)
1010 1111 0110 0101 = -20,634 Jun 26 19:53 UTC (GMT)
1100 1101 1100 1001 = -12,854 Jun 26 19:52 UTC (GMT)
0011 1000 0101 0001 1011 0110 1111 1100 = 944,879,356 Jun 26 19:52 UTC (GMT)
0000 0000 0000 0000 0000 0100 0010 0100 0010 0011 1000 0010 0000 0100 1001 1111 = 4,553,261,057,183 Jun 26 19:49 UTC (GMT)
1001 1001 0000 0000 0000 0000 0000 0000 = -1,728,053,247 Jun 26 19:46 UTC (GMT)
0110 1101 0100 0001 = 27,969 Jun 26 19:43 UTC (GMT)
0110 0110 0110 1011 = 26,219 Jun 26 19:42 UTC (GMT)
0011 0010 0001 0000 = 12,816 Jun 26 19:39 UTC (GMT)
1010 0100 1101 0010 1010 0100 1100 0011 = -1,529,699,132 Jun 26 19:38 UTC (GMT)
1010 0100 = -91 Jun 26 19:38 UTC (GMT)
1001 1010 = -101 Jun 26 19:37 UTC (GMT)
All the converted signed binary one's complement numbers

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

To understand how to convert a signed 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 signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
  • Get the binary representation of the positive number, flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
    !(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 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 by increasing each corresonding power of 2 by exactly one unit:
  • powers of 2: 7 6 5 4 3 2 1 0
    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 adding all the terms up:

    0110 0010(2) =


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


    (0 + 64 + 32 + 0 + 0 + 0 + 2 + 0)(10) =


    (64 + 32 + 2)(10) =


    98(10)

  • Signed binary number in one's complement representation, 1001 1110 = -98(10), a signed negative integer in base 10