Two's Complement: Integer ↗ Binary: 1 190 112 520 884 487 100 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 1 190 112 520 884 487 100(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;
  • 1 190 112 520 884 487 100 ÷ 2 = 595 056 260 442 243 550 + 0;
  • 595 056 260 442 243 550 ÷ 2 = 297 528 130 221 121 775 + 0;
  • 297 528 130 221 121 775 ÷ 2 = 148 764 065 110 560 887 + 1;
  • 148 764 065 110 560 887 ÷ 2 = 74 382 032 555 280 443 + 1;
  • 74 382 032 555 280 443 ÷ 2 = 37 191 016 277 640 221 + 1;
  • 37 191 016 277 640 221 ÷ 2 = 18 595 508 138 820 110 + 1;
  • 18 595 508 138 820 110 ÷ 2 = 9 297 754 069 410 055 + 0;
  • 9 297 754 069 410 055 ÷ 2 = 4 648 877 034 705 027 + 1;
  • 4 648 877 034 705 027 ÷ 2 = 2 324 438 517 352 513 + 1;
  • 2 324 438 517 352 513 ÷ 2 = 1 162 219 258 676 256 + 1;
  • 1 162 219 258 676 256 ÷ 2 = 581 109 629 338 128 + 0;
  • 581 109 629 338 128 ÷ 2 = 290 554 814 669 064 + 0;
  • 290 554 814 669 064 ÷ 2 = 145 277 407 334 532 + 0;
  • 145 277 407 334 532 ÷ 2 = 72 638 703 667 266 + 0;
  • 72 638 703 667 266 ÷ 2 = 36 319 351 833 633 + 0;
  • 36 319 351 833 633 ÷ 2 = 18 159 675 916 816 + 1;
  • 18 159 675 916 816 ÷ 2 = 9 079 837 958 408 + 0;
  • 9 079 837 958 408 ÷ 2 = 4 539 918 979 204 + 0;
  • 4 539 918 979 204 ÷ 2 = 2 269 959 489 602 + 0;
  • 2 269 959 489 602 ÷ 2 = 1 134 979 744 801 + 0;
  • 1 134 979 744 801 ÷ 2 = 567 489 872 400 + 1;
  • 567 489 872 400 ÷ 2 = 283 744 936 200 + 0;
  • 283 744 936 200 ÷ 2 = 141 872 468 100 + 0;
  • 141 872 468 100 ÷ 2 = 70 936 234 050 + 0;
  • 70 936 234 050 ÷ 2 = 35 468 117 025 + 0;
  • 35 468 117 025 ÷ 2 = 17 734 058 512 + 1;
  • 17 734 058 512 ÷ 2 = 8 867 029 256 + 0;
  • 8 867 029 256 ÷ 2 = 4 433 514 628 + 0;
  • 4 433 514 628 ÷ 2 = 2 216 757 314 + 0;
  • 2 216 757 314 ÷ 2 = 1 108 378 657 + 0;
  • 1 108 378 657 ÷ 2 = 554 189 328 + 1;
  • 554 189 328 ÷ 2 = 277 094 664 + 0;
  • 277 094 664 ÷ 2 = 138 547 332 + 0;
  • 138 547 332 ÷ 2 = 69 273 666 + 0;
  • 69 273 666 ÷ 2 = 34 636 833 + 0;
  • 34 636 833 ÷ 2 = 17 318 416 + 1;
  • 17 318 416 ÷ 2 = 8 659 208 + 0;
  • 8 659 208 ÷ 2 = 4 329 604 + 0;
  • 4 329 604 ÷ 2 = 2 164 802 + 0;
  • 2 164 802 ÷ 2 = 1 082 401 + 0;
  • 1 082 401 ÷ 2 = 541 200 + 1;
  • 541 200 ÷ 2 = 270 600 + 0;
  • 270 600 ÷ 2 = 135 300 + 0;
  • 135 300 ÷ 2 = 67 650 + 0;
  • 67 650 ÷ 2 = 33 825 + 0;
  • 33 825 ÷ 2 = 16 912 + 1;
  • 16 912 ÷ 2 = 8 456 + 0;
  • 8 456 ÷ 2 = 4 228 + 0;
  • 4 228 ÷ 2 = 2 114 + 0;
  • 2 114 ÷ 2 = 1 057 + 0;
  • 1 057 ÷ 2 = 528 + 1;
  • 528 ÷ 2 = 264 + 0;
  • 264 ÷ 2 = 132 + 0;
  • 132 ÷ 2 = 66 + 0;
  • 66 ÷ 2 = 33 + 0;
  • 33 ÷ 2 = 16 + 1;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 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.


1 190 112 520 884 487 100(10) = 1 0000 1000 0100 0010 0001 0000 1000 0100 0010 0001 0000 1000 0011 1011 1100(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 61.

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, 61,

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 1 190 112 520 884 487 100(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:

1 190 112 520 884 487 100(10) = 0001 0000 1000 0100 0010 0001 0000 1000 0100 0010 0001 0000 1000 0011 1011 1100

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 1 190 112 520 884 487 099 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 1 190 112 520 884 487 101 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