Signed Binary in Two's (2's) Complement Representation to Decimal Converter

Use the calculator below to convert signed binary in two's (2'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 two's (2's) complement representation to a decimal:

1) In a signed binary in two's (2's) complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.

2) Get the signed binary representation in one's complement, subtract 1 from the initial binary number.

3) 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.

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

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

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

The Latest Signed Binary in Two's (2's) Complement Representation Converted to Decimal

Convert 1010 1110, signed binary in two's (2's) complement representation on 8 bit, to decimal May 21 18:02 UTC (GMT)
Convert 1010 1110, signed binary in two's (2's) complement representation on 8 bit, to decimal May 21 18:00 UTC (GMT)
Convert 0100 0110, signed binary in two's (2's) complement representation on 8 bit, to decimal May 21 17:58 UTC (GMT)
Convert 0010 0100 1010 1010, signed binary in two's (2's) complement representation on 16 bit, to decimal May 21 17:47 UTC (GMT)
Convert 1111 1111 1111 1111 1111 1111 1111 0111, signed binary in two's (2's) complement representation on 32 bit, to decimal May 21 17:19 UTC (GMT)
Convert 1011 1001, signed binary in two's (2's) complement representation on 8 bit, to decimal May 21 17:13 UTC (GMT)
Convert 1100 0011, signed binary in two's (2's) complement representation on 8 bit, to decimal May 21 16:51 UTC (GMT)
Convert 1011 0100 0000 0101, signed binary in two's (2's) complement representation on 16 bit, to decimal May 21 16:37 UTC (GMT)
Convert 1101 0010, signed binary in two's (2's) complement representation on 8 bit, to decimal May 21 15:54 UTC (GMT)
Convert 1011 1101 0101 0110, signed binary in two's (2's) complement representation on 16 bit, to decimal May 21 15:22 UTC (GMT)
» Calculations Performed by Our Visitors: Signed binary numbers in two's (2's) complement representation converted to decimal. Data organized on a Monthly Basis

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

To understand how to convert a signed binary number in two's complement representation from the binary system to decimal (base ten), the easiest way is to do it by an example - convert binary, 1101 1110, to base ten:

  • In a signed binary two's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
  • Get the signed binary representation in one's complement, subtract 1 from the initial number:
    1101 1110 - 1 = 1101 1101
  • 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:
    !(1101 1101) = 0010 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, increasing each corresonding power of 2 by exactly one unit:
  • powers of 2: 7 6 5 4 3 2 1 0
    digits: 0 0 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:

    0010 0010(2) =

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

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

    (32 + 2)(10) =

    34(10)

  • Signed binary number in two's complement representation, 1101 1110 = -34(10), a signed negative integer in base 10.

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