Convert 10 000 110 996 to a signed binary in two's complement representation, from a signed integer number in base 10 decimal system

10 000 110 996(10) to a signed binary two's complement representation = ?

1. 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;
  • 10 000 110 996 ÷ 2 = 5 000 055 498 + 0;
  • 5 000 055 498 ÷ 2 = 2 500 027 749 + 0;
  • 2 500 027 749 ÷ 2 = 1 250 013 874 + 1;
  • 1 250 013 874 ÷ 2 = 625 006 937 + 0;
  • 625 006 937 ÷ 2 = 312 503 468 + 1;
  • 312 503 468 ÷ 2 = 156 251 734 + 0;
  • 156 251 734 ÷ 2 = 78 125 867 + 0;
  • 78 125 867 ÷ 2 = 39 062 933 + 1;
  • 39 062 933 ÷ 2 = 19 531 466 + 1;
  • 19 531 466 ÷ 2 = 9 765 733 + 0;
  • 9 765 733 ÷ 2 = 4 882 866 + 1;
  • 4 882 866 ÷ 2 = 2 441 433 + 0;
  • 2 441 433 ÷ 2 = 1 220 716 + 1;
  • 1 220 716 ÷ 2 = 610 358 + 0;
  • 610 358 ÷ 2 = 305 179 + 0;
  • 305 179 ÷ 2 = 152 589 + 1;
  • 152 589 ÷ 2 = 76 294 + 1;
  • 76 294 ÷ 2 = 38 147 + 0;
  • 38 147 ÷ 2 = 19 073 + 1;
  • 19 073 ÷ 2 = 9 536 + 1;
  • 9 536 ÷ 2 = 4 768 + 0;
  • 4 768 ÷ 2 = 2 384 + 0;
  • 2 384 ÷ 2 = 1 192 + 0;
  • 1 192 ÷ 2 = 596 + 0;
  • 596 ÷ 2 = 298 + 0;
  • 298 ÷ 2 = 149 + 0;
  • 149 ÷ 2 = 74 + 1;
  • 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;

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

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

10 000 110 996(10) = 10 0101 0100 0000 1101 1001 0101 1001 0100(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 34.

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, 34,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


is: 64.


4. Positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64:

10 000 110 996(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0101 0100 0000 1101 1001 0101 1001 0100


Number 10 000 110 996, a signed integer, converted from decimal system (base 10) to a signed binary two's complement representation:

10 000 110 996(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0101 0100 0000 1101 1001 0101 1001 0100

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


More operations of this kind:

10 000 110 995 = ? | 10 000 110 997 = ?


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

10,000,110,996 to signed binary two's complement = ? Sep 20 01:51 UTC (GMT)
1,105 to signed binary two's complement = ? Sep 20 01:50 UTC (GMT)
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10,000,000,965 to signed binary two's complement = ? Sep 20 01:50 UTC (GMT)
244 to signed binary two's complement = ? Sep 20 01:50 UTC (GMT)
8,820 to signed binary two's complement = ? Sep 20 01:49 UTC (GMT)
12,582,937 to signed binary two's complement = ? Sep 20 01:49 UTC (GMT)
87 to signed binary two's complement = ? Sep 20 01:49 UTC (GMT)
109,956 to signed binary two's complement = ? Sep 20 01:49 UTC (GMT)
-104,710 to signed binary two's complement = ? Sep 20 01:49 UTC (GMT)
-41,327 to signed binary two's complement = ? Sep 20 01:49 UTC (GMT)
-534,874 to signed binary two's complement = ? Sep 20 01:49 UTC (GMT)
-2,013,265,918 to signed binary two's complement = ? Sep 20 01:49 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