Signed binary one's complement number 0111 1011 converted to decimal system (base ten) signed integer

How to convert a signed binary one's complement:
0111 1011(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.

0111 1011 is the binary representation of a positive integer, on 8 bits.


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:

* Not the case *


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

    • 27

      0

    • 26

      1

    • 25

      1

    • 24

      1

    • 23

      1

    • 22

      0

    • 21

      1

    • 20

      1

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

0111 1011(2) =

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

(0 + 64 + 32 + 16 + 8 + 0 + 2 + 1)(10) =

(64 + 32 + 16 + 8 + 2 + 1)(10) =

123(10)

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

0111 1011(2) = 123(10)

Conclusion:
Number 0111 1011(2) converted from signed binary one's complement representation to an integer in decimal system (in base 10):

0111 1011(2) = 123(10)

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

More operations of this kind:

0111 1010 = ?

0111 1100 = ?


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)

0111 1011 = 123 Jan 26 12:53 UTC (GMT)
0100 0101 0101 0111 = 17,751 Jan 26 12:50 UTC (GMT)
0000 0110 0110 1110 = 1,646 Jan 26 12:49 UTC (GMT)
0101 0101 0101 0100 = 21,844 Jan 26 12:49 UTC (GMT)
1100 0000 1001 1111 1111 1111 1111 1111 = -1,063,256,064 Jan 26 12:49 UTC (GMT)
0000 0001 0111 0111 = 375 Jan 26 12:46 UTC (GMT)
1100 0111 = -56 Jan 26 12:46 UTC (GMT)
1100 0001 1111 0000 0000 0000 0000 0100 = -1,041,235,963 Jan 26 12:40 UTC (GMT)
1111 1110 1000 0101 = -378 Jan 26 12:38 UTC (GMT)
1101 1100 0001 0101 0001 1101 0011 0111 = -602,596,040 Jan 26 12:38 UTC (GMT)
0100 0000 1000 1011 1001 1110 1010 0111 = 1,082,891,943 Jan 26 12:38 UTC (GMT)
0000 0000 0000 1111 1111 0000 0001 0100 = 1,044,500 Jan 26 12:36 UTC (GMT)
0000 0000 0000 0111 1111 0000 0000 0100 0000 0000 0000 0000 0000 0000 0001 0000 = 2,234,224,807,510,032 Jan 26 12:36 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