Signed binary one's complement number 1101 0110 converted to decimal system (base ten) signed integer

Signed binary one's complement 1101 0110(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.

1101 0110 is the binary representation of a negative 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:

!(1101 0110) = 0010 1001


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

    • 27

      0

    • 26

      0

    • 25

      1

    • 24

      0

    • 23

      1

    • 22

      0

    • 21

      0

    • 20

      1

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

0010 1001(2) =

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

(0 + 0 + 32 + 0 + 8 + 0 + 0 + 1)(10) =

(32 + 8 + 1)(10) =

41(10)

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

1101 0110(2) = -41(10)

Number 1101 0110(2) converted from signed binary one's complement representation to an integer in decimal system (in base 10):
1101 0110(2) = -41(10)

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

More operations of this kind:

1101 0101 = ?

1101 0111 = ?


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)

1101 0110 = -41 Apr 18 07:55 UTC (GMT)
0000 0110 1011 0000 = 1,712 Apr 18 07:54 UTC (GMT)
1001 0000 0000 0011 = -28,668 Apr 18 07:54 UTC (GMT)
0000 0000 0000 0000 0000 0000 0000 0010 = 2 Apr 18 07:53 UTC (GMT)
1000 0000 0001 1100 = -32,739 Apr 18 07:53 UTC (GMT)
0000 1111 1111 1111 1110 0000 0111 1010 1010 0110 1111 0100 0010 0010 1100 0011 = 1,152,886,847,021,785,795 Apr 18 07:52 UTC (GMT)
0000 0100 0100 1110 = 1,102 Apr 18 07:52 UTC (GMT)
1100 1001 = -54 Apr 18 07:51 UTC (GMT)
0011 0101 1101 0110 = 13,782 Apr 18 07:51 UTC (GMT)
1100 1001 = -54 Apr 18 07:51 UTC (GMT)
1100 1001 = -54 Apr 18 07:51 UTC (GMT)
0000 1010 0010 0000 = 2,592 Apr 18 07:51 UTC (GMT)
0101 1111 1011 1110 0100 0000 0000 0000 = 1,606,303,744 Apr 18 07:50 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