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)

1011 1011 1011 1011 = -17,476 Jul 23 11:42 UTC (GMT)
1001 1101 = -98 Jul 23 11:41 UTC (GMT)
1111 0101 = -10 Jul 23 11:41 UTC (GMT)
0000 0011 1011 0011 = 947 Jul 23 11:33 UTC (GMT)
0000 0011 1000 1011 = 907 Jul 23 11:21 UTC (GMT)
0010 1101 = 45 Jul 23 11:01 UTC (GMT)
1100 1110 = -49 Jul 23 10:32 UTC (GMT)
1110 1100 1000 1001 = -4,982 Jul 23 10:30 UTC (GMT)
0010 1000 = 40 Jul 23 10:29 UTC (GMT)
1100 1101 0101 1110 = -12,961 Jul 23 10:18 UTC (GMT)
0101 0011 = 83 Jul 23 10:17 UTC (GMT)
0000 0000 0011 1111 1111 1111 1111 1111 = 4,194,303 Jul 23 10:14 UTC (GMT)
0111 0001 = 113 Jul 23 10:07 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