Convert -1 985 229 339 to a signed binary in two's complement representation, from a signed integer number in base 10 decimal system

-1 985 229 339(10) to a signed binary two's complement representation = ?

1. Start with the positive version of the number:

|-1 985 229 339| = 1 985 229 339

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;
  • 1 985 229 339 ÷ 2 = 992 614 669 + 1;
  • 992 614 669 ÷ 2 = 496 307 334 + 1;
  • 496 307 334 ÷ 2 = 248 153 667 + 0;
  • 248 153 667 ÷ 2 = 124 076 833 + 1;
  • 124 076 833 ÷ 2 = 62 038 416 + 1;
  • 62 038 416 ÷ 2 = 31 019 208 + 0;
  • 31 019 208 ÷ 2 = 15 509 604 + 0;
  • 15 509 604 ÷ 2 = 7 754 802 + 0;
  • 7 754 802 ÷ 2 = 3 877 401 + 0;
  • 3 877 401 ÷ 2 = 1 938 700 + 1;
  • 1 938 700 ÷ 2 = 969 350 + 0;
  • 969 350 ÷ 2 = 484 675 + 0;
  • 484 675 ÷ 2 = 242 337 + 1;
  • 242 337 ÷ 2 = 121 168 + 1;
  • 121 168 ÷ 2 = 60 584 + 0;
  • 60 584 ÷ 2 = 30 292 + 0;
  • 30 292 ÷ 2 = 15 146 + 0;
  • 15 146 ÷ 2 = 7 573 + 0;
  • 7 573 ÷ 2 = 3 786 + 1;
  • 3 786 ÷ 2 = 1 893 + 0;
  • 1 893 ÷ 2 = 946 + 1;
  • 946 ÷ 2 = 473 + 0;
  • 473 ÷ 2 = 236 + 1;
  • 236 ÷ 2 = 118 + 0;
  • 118 ÷ 2 = 59 + 0;
  • 59 ÷ 2 = 29 + 1;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.

1 985 229 339(10) = 111 0110 0101 0100 0011 0010 0001 1011(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:

1 985 229 339(10) = 0111 0110 0101 0100 0011 0010 0001 1011


6. Get the negative integer number representation. Part 1:

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)


!(0111 0110 0101 0100 0011 0010 0001 1011) =


1000 1001 1010 1011 1100 1101 1110 0100


7. Get the negative integer number representation. Part 2:

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


signed binary two's complement,


add 1 to the number calculated above


1000 1001 1010 1011 1100 1101 1110 0100 + 1 =


1000 1001 1010 1011 1100 1101 1110 0101


Number -1 985 229 339, a signed integer, converted from decimal system (base 10) to a signed binary two's complement representation:

-1 985 229 339(10) = 1000 1001 1010 1011 1100 1101 1110 0101

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


More operations of this kind:

-1 985 229 340 = ? | -1 985 229 338 = ?


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

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

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

5) Only if the initial number is negative, add 1 to the number at the previous point.

Latest signed integers converted from decimal system to binary two's complement representation

-1,985,229,339 to signed binary two's complement = ? Apr 14 11:48 UTC (GMT)
1,476 to signed binary two's complement = ? Apr 14 11:48 UTC (GMT)
10 to signed binary two's complement = ? Apr 14 11:48 UTC (GMT)
139,948,407,982,522 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT)
-2,100,261,239 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT)
20 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT)
-342,529 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT)
-278 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT)
100,111 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT)
100,111 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT)
-2,865 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT)
10 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT)
-342,558 to signed binary two's complement = ? Apr 14 11:45 UTC (GMT)
All decimal integer numbers converted to signed binary two's complement representation

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

Follow the steps below to convert a signed base 10 integer number to signed binary in two'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, keeping track of each remainder, until we get a quotient that is 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, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will 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 1s and all 1 bits with 0s (reversing the digits).
  • 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

  • 1. Start with the positive version of the number: |-60| = 60
  • 2. Divide repeatedly 60 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 60 ÷ 2 = 30 + 0
    • 30 ÷ 2 = 15 + 0
    • 15 ÷ 2 = 7 + 1
    • 7 ÷ 2 = 3 + 1
    • 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:
    60(10) = 11 1100(2)
  • 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
    60(10) = 0011 1100(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
    !(0011 1100) = 1100 0011
  • 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
    -60(10) = 1100 0011 + 1 = 1100 0100
  • Number -60(10), signed integer, converted from decimal system (base 10) to signed binary two's complement representation = 1100 0100