Two's Complement: Integer ↗ Binary: 11 011 110 110 087 Convert the Integer Number to a Signed Binary in Two's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 11 011 110 110 087(10) converted and written as a signed binary in two's complement representation (base 2) = ?

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;
  • 11 011 110 110 087 ÷ 2 = 5 505 555 055 043 + 1;
  • 5 505 555 055 043 ÷ 2 = 2 752 777 527 521 + 1;
  • 2 752 777 527 521 ÷ 2 = 1 376 388 763 760 + 1;
  • 1 376 388 763 760 ÷ 2 = 688 194 381 880 + 0;
  • 688 194 381 880 ÷ 2 = 344 097 190 940 + 0;
  • 344 097 190 940 ÷ 2 = 172 048 595 470 + 0;
  • 172 048 595 470 ÷ 2 = 86 024 297 735 + 0;
  • 86 024 297 735 ÷ 2 = 43 012 148 867 + 1;
  • 43 012 148 867 ÷ 2 = 21 506 074 433 + 1;
  • 21 506 074 433 ÷ 2 = 10 753 037 216 + 1;
  • 10 753 037 216 ÷ 2 = 5 376 518 608 + 0;
  • 5 376 518 608 ÷ 2 = 2 688 259 304 + 0;
  • 2 688 259 304 ÷ 2 = 1 344 129 652 + 0;
  • 1 344 129 652 ÷ 2 = 672 064 826 + 0;
  • 672 064 826 ÷ 2 = 336 032 413 + 0;
  • 336 032 413 ÷ 2 = 168 016 206 + 1;
  • 168 016 206 ÷ 2 = 84 008 103 + 0;
  • 84 008 103 ÷ 2 = 42 004 051 + 1;
  • 42 004 051 ÷ 2 = 21 002 025 + 1;
  • 21 002 025 ÷ 2 = 10 501 012 + 1;
  • 10 501 012 ÷ 2 = 5 250 506 + 0;
  • 5 250 506 ÷ 2 = 2 625 253 + 0;
  • 2 625 253 ÷ 2 = 1 312 626 + 1;
  • 1 312 626 ÷ 2 = 656 313 + 0;
  • 656 313 ÷ 2 = 328 156 + 1;
  • 328 156 ÷ 2 = 164 078 + 0;
  • 164 078 ÷ 2 = 82 039 + 0;
  • 82 039 ÷ 2 = 41 019 + 1;
  • 41 019 ÷ 2 = 20 509 + 1;
  • 20 509 ÷ 2 = 10 254 + 1;
  • 10 254 ÷ 2 = 5 127 + 0;
  • 5 127 ÷ 2 = 2 563 + 1;
  • 2 563 ÷ 2 = 1 281 + 1;
  • 1 281 ÷ 2 = 640 + 1;
  • 640 ÷ 2 = 320 + 0;
  • 320 ÷ 2 = 160 + 0;
  • 160 ÷ 2 = 80 + 0;
  • 80 ÷ 2 = 40 + 0;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 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.


11 011 110 110 087(10) = 1010 0000 0011 1011 1001 0100 1110 1000 0011 1000 0111(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 44.

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, 44,

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.


Number 11 011 110 110 087(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:

11 011 110 110 087(10) = 0000 0000 0000 0000 0000 1010 0000 0011 1011 1001 0100 1110 1000 0011 1000 0111

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

More operations on integers written as signed binary numbers in two's complement representation:

» Signed integer number 11 011 110 110 086 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

» Signed integer number 11 011 110 110 088 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

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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