Signed binary one's complement number 0010 1010 1100 0111 converted to decimal system (base ten) signed integer

Signed binary one's complement 0010 1010 1100 0111(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.

0010 1010 1100 0111 is the binary representation of a positive 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:

* Not the case *


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

      0
    • 211

      1
    • 210

      0
    • 29

      1
    • 28

      0
    • 27

      1
    • 26

      1
    • 25

      0
    • 24

      0
    • 23

      0
    • 22

      1
    • 21

      1
    • 20

      1

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

0010 1010 1100 0111(2) =


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


(0 + 0 + 8 192 + 0 + 2 048 + 0 + 512 + 0 + 128 + 64 + 0 + 0 + 0 + 4 + 2 + 1)(10) =


(8 192 + 2 048 + 512 + 128 + 64 + 4 + 2 + 1)(10) =


10 951(10)

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

0010 1010 1100 0111(2) = 10 951(10)

Number 0010 1010 1100 0111(2) converted from signed binary one's complement representation to an integer in decimal system (in base 10):
0010 1010 1100 0111(2) = 10 951(10)

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


More operations of this kind:

0010 1010 1100 0110 = ?

0010 1010 1100 1000 = ?


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)

0010 1010 1100 0111 = 10,951 Feb 24 16:59 UTC (GMT)
1000 1100 0001 0000 0111 1111 1111 1110 = -1,945,075,713 Feb 24 16:59 UTC (GMT)
1011 1001 1011 0011 = -17,996 Feb 24 16:59 UTC (GMT)
0000 0100 0000 0011 = 1,027 Feb 24 16:58 UTC (GMT)
1111 1000 0101 0001 = -1,966 Feb 24 16:58 UTC (GMT)
0111 0101 0001 1010 = 29,978 Feb 24 16:58 UTC (GMT)
1111 1010 0000 1101 = -1,522 Feb 24 16:57 UTC (GMT)
0000 0000 0000 0110 0110 0110 0110 1000 = 419,432 Feb 24 16:57 UTC (GMT)
0000 1101 1011 1111 = 3,519 Feb 24 16:57 UTC (GMT)
0000 1000 1100 0000 = 2,240 Feb 24 16:56 UTC (GMT)
0000 1101 0100 1110 = 3,406 Feb 24 16:55 UTC (GMT)
1011 0101 0011 1110 = -19,137 Feb 24 16:55 UTC (GMT)
1111 1000 0010 1100 = -2,003 Feb 24 16:55 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