Signed: Integer ↗ Binary: -2 991 006 890 006 229 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number -2 991 006 890 006 229(10)
converted and written as a signed binary (base 2) = ?

1. Start with the positive version of the number:

|-2 991 006 890 006 229| = 2 991 006 890 006 229

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;
  • 2 991 006 890 006 229 ÷ 2 = 1 495 503 445 003 114 + 1;
  • 1 495 503 445 003 114 ÷ 2 = 747 751 722 501 557 + 0;
  • 747 751 722 501 557 ÷ 2 = 373 875 861 250 778 + 1;
  • 373 875 861 250 778 ÷ 2 = 186 937 930 625 389 + 0;
  • 186 937 930 625 389 ÷ 2 = 93 468 965 312 694 + 1;
  • 93 468 965 312 694 ÷ 2 = 46 734 482 656 347 + 0;
  • 46 734 482 656 347 ÷ 2 = 23 367 241 328 173 + 1;
  • 23 367 241 328 173 ÷ 2 = 11 683 620 664 086 + 1;
  • 11 683 620 664 086 ÷ 2 = 5 841 810 332 043 + 0;
  • 5 841 810 332 043 ÷ 2 = 2 920 905 166 021 + 1;
  • 2 920 905 166 021 ÷ 2 = 1 460 452 583 010 + 1;
  • 1 460 452 583 010 ÷ 2 = 730 226 291 505 + 0;
  • 730 226 291 505 ÷ 2 = 365 113 145 752 + 1;
  • 365 113 145 752 ÷ 2 = 182 556 572 876 + 0;
  • 182 556 572 876 ÷ 2 = 91 278 286 438 + 0;
  • 91 278 286 438 ÷ 2 = 45 639 143 219 + 0;
  • 45 639 143 219 ÷ 2 = 22 819 571 609 + 1;
  • 22 819 571 609 ÷ 2 = 11 409 785 804 + 1;
  • 11 409 785 804 ÷ 2 = 5 704 892 902 + 0;
  • 5 704 892 902 ÷ 2 = 2 852 446 451 + 0;
  • 2 852 446 451 ÷ 2 = 1 426 223 225 + 1;
  • 1 426 223 225 ÷ 2 = 713 111 612 + 1;
  • 713 111 612 ÷ 2 = 356 555 806 + 0;
  • 356 555 806 ÷ 2 = 178 277 903 + 0;
  • 178 277 903 ÷ 2 = 89 138 951 + 1;
  • 89 138 951 ÷ 2 = 44 569 475 + 1;
  • 44 569 475 ÷ 2 = 22 284 737 + 1;
  • 22 284 737 ÷ 2 = 11 142 368 + 1;
  • 11 142 368 ÷ 2 = 5 571 184 + 0;
  • 5 571 184 ÷ 2 = 2 785 592 + 0;
  • 2 785 592 ÷ 2 = 1 392 796 + 0;
  • 1 392 796 ÷ 2 = 696 398 + 0;
  • 696 398 ÷ 2 = 348 199 + 0;
  • 348 199 ÷ 2 = 174 099 + 1;
  • 174 099 ÷ 2 = 87 049 + 1;
  • 87 049 ÷ 2 = 43 524 + 1;
  • 43 524 ÷ 2 = 21 762 + 0;
  • 21 762 ÷ 2 = 10 881 + 0;
  • 10 881 ÷ 2 = 5 440 + 1;
  • 5 440 ÷ 2 = 2 720 + 0;
  • 2 720 ÷ 2 = 1 360 + 0;
  • 1 360 ÷ 2 = 680 + 0;
  • 680 ÷ 2 = 340 + 0;
  • 340 ÷ 2 = 170 + 0;
  • 170 ÷ 2 = 85 + 0;
  • 85 ÷ 2 = 42 + 1;
  • 42 ÷ 2 = 21 + 0;
  • 21 ÷ 2 = 10 + 1;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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.


2 991 006 890 006 229(10) = 1010 1010 0000 0100 1110 0000 1111 0011 0011 0001 0110 1101 0101(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 52.


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) is reserved for 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, 52,

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


=== is: 64.


5. 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:


2 991 006 890 006 229(10) = 0000 0000 0000 1010 1010 0000 0100 1110 0000 1111 0011 0011 0001 0110 1101 0101


6. Get the negative integer number representation:

To get the negative integer number representation on 64 bits (8 Bytes),


... change the first bit (the leftmost), from 0 to 1...


Number -2 991 006 890 006 229(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-2 991 006 890 006 229(10) = 1000 0000 0000 1010 1010 0000 0100 1110 0000 1111 0011 0011 0001 0110 1101 0101

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

The latest signed integer numbers (that are written in decimal system, in base ten) converted and written as signed binary numbers

How to convert signed integers from decimal system to binary code system

Follow the steps below to convert a signed base ten integer number to signed binary:

  • 1. In a signed binary, first bit (the leftmost) is reserved for sign: 0 = positive integer number, 1 = positive integer number. If the number to be converted is negative, start with its positive version.
  • 2. Divide repeatedly by 2 the positive integer number keeping track of each remainder. STOP when 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 have a length of 4, 8, 16, 32, 64, ... bits (power of 2) - if needed, fill in extra '0' bits in front of the base 2 number (to the left), up to the right length; this way the first bit (the leftmost one) is always '0', as for a positive representation.
  • 5. To get the negative reprezentation of the number, simply switch the first bit (the leftmost one), from '0' to '1'.

Example: convert the negative number -63 from decimal system (base ten) to signed binary code system:

  • 1. Start with the positive version of the number: |-63| = 63;
  • 2. Divide repeatedly 63 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder
    • 63 ÷ 2 = 31 + 1
    • 31 ÷ 2 = 15 + 1
    • 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:
    63(10) = 11 1111(2)
  • 4. The actual length of base 2 representation number is 6, so the positive binary computer representation length of the signed binary will take in this case 8 bits (the least power of 2 higher than 6) - add extra '0's in front (to the left), up to the required length; this way the first bit (the leftmost one) is to be '0', as for a positive number:
    63(10) = 0011 1111(2)
  • 5. To get the negative integer number representation simply change the first bit (the leftmost), from '0' to '1':
    -63(10) = 1011 1111
  • Number -63(10), signed integer, converted from decimal system (base 10) to signed binary = 1011 1111