Convert -1 247 092 983 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

-1 247 092 983(10) to a signed binary one's complement representation = ?

1. Start with the positive version of the number:

|-1 247 092 983| = 1 247 092 983

2. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

  • division = quotient + remainder;
  • 1 247 092 983 ÷ 2 = 623 546 491 + 1;
  • 623 546 491 ÷ 2 = 311 773 245 + 1;
  • 311 773 245 ÷ 2 = 155 886 622 + 1;
  • 155 886 622 ÷ 2 = 77 943 311 + 0;
  • 77 943 311 ÷ 2 = 38 971 655 + 1;
  • 38 971 655 ÷ 2 = 19 485 827 + 1;
  • 19 485 827 ÷ 2 = 9 742 913 + 1;
  • 9 742 913 ÷ 2 = 4 871 456 + 1;
  • 4 871 456 ÷ 2 = 2 435 728 + 0;
  • 2 435 728 ÷ 2 = 1 217 864 + 0;
  • 1 217 864 ÷ 2 = 608 932 + 0;
  • 608 932 ÷ 2 = 304 466 + 0;
  • 304 466 ÷ 2 = 152 233 + 0;
  • 152 233 ÷ 2 = 76 116 + 1;
  • 76 116 ÷ 2 = 38 058 + 0;
  • 38 058 ÷ 2 = 19 029 + 0;
  • 19 029 ÷ 2 = 9 514 + 1;
  • 9 514 ÷ 2 = 4 757 + 0;
  • 4 757 ÷ 2 = 2 378 + 1;
  • 2 378 ÷ 2 = 1 189 + 0;
  • 1 189 ÷ 2 = 594 + 1;
  • 594 ÷ 2 = 297 + 0;
  • 297 ÷ 2 = 148 + 1;
  • 148 ÷ 2 = 74 + 0;
  • 74 ÷ 2 = 37 + 0;
  • 37 ÷ 2 = 18 + 1;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

1 247 092 983(10) = 100 1010 0101 0101 0010 0000 1111 0111(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 31.

A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...

First bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

The least number that is:

a power of 2

and is larger than the actual length, 31,

so that the first bit (leftmost) could be zero

(we deal with a positive number at this moment)

is: 32.


5. Positive binary computer representation on 32 bits (4 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:

1 247 092 983(10) = 0100 1010 0101 0101 0010 0000 1111 0111


6. Get the negative integer number representation:

To get the negative integer number representation on 32 bits (4 Bytes),

signed binary one's complement,

replace all the bits on 0 with 1s

and all the bits set on 1 with 0s

(reverse the digits, flip the digits)


!(0100 1010 0101 0101 0010 0000 1111 0111) =

1011 0101 1010 1010 1101 1111 0000 1000


Number -1 247 092 983, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

-1 247 092 983(10) = 1011 0101 1010 1010 1101 1111 0000 1000

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

More operations of this kind:

-1 247 092 984 = ? | -1 247 092 982 = ?


Convert signed integer numbers from the decimal system (base ten) to signed binary one's complement representation

How to convert a base 10 signed integer number to signed binary in one's complement representation:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is 0.

2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.

3) Construct the positive binary computer representation so that the first bit is 0.

4) Only if the initial number is negative, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).

Latest signed integer numbers converted from decimal system to signed binary in one's complement representation

-1,247,092,983 to signed binary one's complement = ? Mar 08 12:47 UTC (GMT)
-4,689 to signed binary one's complement = ? Mar 08 12:47 UTC (GMT)
-67 to signed binary one's complement = ? Mar 08 12:47 UTC (GMT)
1,027 to signed binary one's complement = ? Mar 08 12:46 UTC (GMT)
2,607 to signed binary one's complement = ? Mar 08 12:46 UTC (GMT)
1,011,101 to signed binary one's complement = ? Mar 08 12:45 UTC (GMT)
101,005 to signed binary one's complement = ? Mar 08 12:45 UTC (GMT)
19,216,818 to signed binary one's complement = ? Mar 08 12:45 UTC (GMT)
-32,550 to signed binary one's complement = ? Mar 08 12:44 UTC (GMT)
-5,282 to signed binary one's complement = ? Mar 08 12:44 UTC (GMT)
5,424 to signed binary one's complement = ? Mar 08 12:43 UTC (GMT)
100,111 to signed binary one's complement = ? Mar 08 12:42 UTC (GMT)
79,939 to signed binary one's complement = ? Mar 08 12:42 UTC (GMT)
All decimal integer numbers converted to signed binary one's complement representation

How to convert signed integers from the decimal system to signed binary in one's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to ZERO.
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 3 ÷ 2 = 1 + 1
    • 1 ÷ 2 = 0 + 1
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110

    • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110