Signed binary one's complement number 1100 0011 0011 1100 converted to decimal system (base ten) signed integer

How to convert a signed binary one's complement:
1100 0011 0011 1100(2)
to an integer in decimal system (in base 10)

1. Is this a positive or a negative number?


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

1100 0011 0011 1100 is the binary representation of a negative integer, on 16 bits (2 Bytes).


2. Get the binary representation of the positive (unsigned) number:


* Run this step only if the number is negative *

Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:

!(1100 0011 0011 1100) = 0011 1100 1100 0011


3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

    • 215

      0

    • 214

      0

    • 213

      1

    • 212

      1

    • 211

      1

    • 210

      1

    • 29

      0

    • 28

      0

    • 27

      1

    • 26

      1

    • 25

      0

    • 24

      0

    • 23

      0

    • 22

      0

    • 21

      1

    • 20

      1

4. Multiply each bit by its corresponding power of 2 and add all the terms up:

0011 1100 1100 0011(2) =

(0 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =

(0 + 0 + 8 192 + 4 096 + 2 048 + 1 024 + 0 + 0 + 128 + 64 + 0 + 0 + 0 + 0 + 2 + 1)(10) =

(8 192 + 4 096 + 2 048 + 1 024 + 128 + 64 + 2 + 1)(10) =

15 555(10)

5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:

1100 0011 0011 1100(2) = -15 555(10)

Conclusion:
Number 1100 0011 0011 1100(2) converted from signed binary one's complement representation to an integer in decimal system (in base 10):

1100 0011 0011 1100(2) = -15 555(10)

Spaces used to group digits: for binary, by 4; for decimal, by 3.

More operations of this kind:

1100 0011 0011 1011 = ?

1100 0011 0011 1101 = ?


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 0011 0011 1100 = -15,555 Jan 26 18:37 UTC (GMT)
1110 0000 = -31 Jan 26 18:36 UTC (GMT)
0100 0011 0111 1001 = 17,273 Jan 26 18:36 UTC (GMT)
0010 1100 0111 1101 = 11,389 Jan 26 18:36 UTC (GMT)
0100 0000 0101 1100 1100 1100 1100 1110 = 1,079,823,566 Jan 26 18:35 UTC (GMT)
1000 0000 0000 0000 0000 0000 0000 0000 0001 0000 1101 0110 0011 1010 1110 1000 = -9,223,372,036,572,300,567 Jan 26 18:35 UTC (GMT)
0000 0101 0101 0001 = 1,361 Jan 26 18:32 UTC (GMT)
1010 = -5 Jan 26 18:30 UTC (GMT)
0110 0101 = 101 Jan 26 18:30 UTC (GMT)
0000 0001 0111 1111 = 383 Jan 26 18:28 UTC (GMT)
1000 1010 1100 0111 = -30,008 Jan 26 18:28 UTC (GMT)
1011 1110 0100 1110 = -16,817 Jan 26 18:24 UTC (GMT)
0000 0111 0011 0111 = 1,847 Jan 26 18:21 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