Signed Binary in One's (1's) Complement Representation to Decimal Converter

Use the calculator below to convert signed binary in one's (1's) complement representation to decimal

Binary number's length must be: 2, 4, 8, 16, 32, 64 - or else extra bits on 0 are added in front (to the left).

How to convert a signed binary in one's (1's) complement representation to a decimal:

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

2) Construct the unsigned binary number: flip all the bits in the signed binary in 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 to get the positive integer number in base ten.

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

The Latest Signed Binary in One's (1's) Complement Representation Converted to Decimal

Convert 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1000 1000, signed binary in one's (1's) complement representation on 64 bit, to decimal Jan 31 19:48 UTC (GMT)
Convert 1000 0111 0000 0100, signed binary in one's (1's) complement representation on 16 bit, to decimal Jan 31 19:48 UTC (GMT)
Convert 1100 0000 0010 1010, signed binary in one's (1's) complement representation on 16 bit, to decimal Jan 31 19:47 UTC (GMT)
Convert 0100 0001 1101 0010, signed binary in one's (1's) complement representation on 16 bit, to decimal Jan 31 19:46 UTC (GMT)
Convert 0011 1111 1000 1000, signed binary in one's (1's) complement representation on 16 bit, to decimal Jan 31 19:46 UTC (GMT)
Convert 0000 0000 0000 0000 0000 0100 0010 0001, signed binary in one's (1's) complement representation on 32 bit, to decimal Jan 31 19:46 UTC (GMT)
Convert 1101 0011, signed binary in one's (1's) complement representation on 8 bit, to decimal Jan 31 19:45 UTC (GMT)
Convert 1000 0101 0101 1100, signed binary in one's (1's) complement representation on 16 bit, to decimal Jan 31 19:43 UTC (GMT)
Convert 0000 0000 0000 1011 1010 1101 0101 1101, signed binary in one's (1's) complement representation on 32 bit, to decimal Jan 31 19:36 UTC (GMT)
Convert 01, signed binary in one's (1's) complement representation on 2 bit, to decimal Jan 31 19:35 UTC (GMT)
» Calculations Performed by Our Visitors: Signed binary numbers in one's (1's) complement representation converted to decimal. Data organized on a Monthly Basis

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

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