Convert 1 011 000 000 000 886 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 1 011 000 000 000 886(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
1 011 000 000 000 886 to a signed binary in two's (2's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

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;
  • 1 011 000 000 000 886 ÷ 2 = 505 500 000 000 443 + 0;
  • 505 500 000 000 443 ÷ 2 = 252 750 000 000 221 + 1;
  • 252 750 000 000 221 ÷ 2 = 126 375 000 000 110 + 1;
  • 126 375 000 000 110 ÷ 2 = 63 187 500 000 055 + 0;
  • 63 187 500 000 055 ÷ 2 = 31 593 750 000 027 + 1;
  • 31 593 750 000 027 ÷ 2 = 15 796 875 000 013 + 1;
  • 15 796 875 000 013 ÷ 2 = 7 898 437 500 006 + 1;
  • 7 898 437 500 006 ÷ 2 = 3 949 218 750 003 + 0;
  • 3 949 218 750 003 ÷ 2 = 1 974 609 375 001 + 1;
  • 1 974 609 375 001 ÷ 2 = 987 304 687 500 + 1;
  • 987 304 687 500 ÷ 2 = 493 652 343 750 + 0;
  • 493 652 343 750 ÷ 2 = 246 826 171 875 + 0;
  • 246 826 171 875 ÷ 2 = 123 413 085 937 + 1;
  • 123 413 085 937 ÷ 2 = 61 706 542 968 + 1;
  • 61 706 542 968 ÷ 2 = 30 853 271 484 + 0;
  • 30 853 271 484 ÷ 2 = 15 426 635 742 + 0;
  • 15 426 635 742 ÷ 2 = 7 713 317 871 + 0;
  • 7 713 317 871 ÷ 2 = 3 856 658 935 + 1;
  • 3 856 658 935 ÷ 2 = 1 928 329 467 + 1;
  • 1 928 329 467 ÷ 2 = 964 164 733 + 1;
  • 964 164 733 ÷ 2 = 482 082 366 + 1;
  • 482 082 366 ÷ 2 = 241 041 183 + 0;
  • 241 041 183 ÷ 2 = 120 520 591 + 1;
  • 120 520 591 ÷ 2 = 60 260 295 + 1;
  • 60 260 295 ÷ 2 = 30 130 147 + 1;
  • 30 130 147 ÷ 2 = 15 065 073 + 1;
  • 15 065 073 ÷ 2 = 7 532 536 + 1;
  • 7 532 536 ÷ 2 = 3 766 268 + 0;
  • 3 766 268 ÷ 2 = 1 883 134 + 0;
  • 1 883 134 ÷ 2 = 941 567 + 0;
  • 941 567 ÷ 2 = 470 783 + 1;
  • 470 783 ÷ 2 = 235 391 + 1;
  • 235 391 ÷ 2 = 117 695 + 1;
  • 117 695 ÷ 2 = 58 847 + 1;
  • 58 847 ÷ 2 = 29 423 + 1;
  • 29 423 ÷ 2 = 14 711 + 1;
  • 14 711 ÷ 2 = 7 355 + 1;
  • 7 355 ÷ 2 = 3 677 + 1;
  • 3 677 ÷ 2 = 1 838 + 1;
  • 1 838 ÷ 2 = 919 + 0;
  • 919 ÷ 2 = 459 + 1;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.

1 011 000 000 000 886(10) = 11 1001 0111 0111 1111 1100 0111 1101 1110 0011 0011 0111 0110(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 50,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the 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.


Decimal Number 1 011 000 000 000 886(10) converted to signed binary in two's complement representation:

1 011 000 000 000 886(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 0111 1101 1110 0011 0011 0111 0110

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

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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