Convert -12 697 160 277 502 to a Signed Binary (Base 2)

How to convert -12 697 160 277 502(10), a signed base 10 integer number? How to write it as a signed binary code in base 2

What are the required steps to convert base 10 integer
number -12 697 160 277 502 to signed binary code (in base 2)?

  • 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. Start with the positive version of the number:

|-12 697 160 277 502| = 12 697 160 277 502

2. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 12 697 160 277 502 ÷ 2 = 6 348 580 138 751 + 0;
  • 6 348 580 138 751 ÷ 2 = 3 174 290 069 375 + 1;
  • 3 174 290 069 375 ÷ 2 = 1 587 145 034 687 + 1;
  • 1 587 145 034 687 ÷ 2 = 793 572 517 343 + 1;
  • 793 572 517 343 ÷ 2 = 396 786 258 671 + 1;
  • 396 786 258 671 ÷ 2 = 198 393 129 335 + 1;
  • 198 393 129 335 ÷ 2 = 99 196 564 667 + 1;
  • 99 196 564 667 ÷ 2 = 49 598 282 333 + 1;
  • 49 598 282 333 ÷ 2 = 24 799 141 166 + 1;
  • 24 799 141 166 ÷ 2 = 12 399 570 583 + 0;
  • 12 399 570 583 ÷ 2 = 6 199 785 291 + 1;
  • 6 199 785 291 ÷ 2 = 3 099 892 645 + 1;
  • 3 099 892 645 ÷ 2 = 1 549 946 322 + 1;
  • 1 549 946 322 ÷ 2 = 774 973 161 + 0;
  • 774 973 161 ÷ 2 = 387 486 580 + 1;
  • 387 486 580 ÷ 2 = 193 743 290 + 0;
  • 193 743 290 ÷ 2 = 96 871 645 + 0;
  • 96 871 645 ÷ 2 = 48 435 822 + 1;
  • 48 435 822 ÷ 2 = 24 217 911 + 0;
  • 24 217 911 ÷ 2 = 12 108 955 + 1;
  • 12 108 955 ÷ 2 = 6 054 477 + 1;
  • 6 054 477 ÷ 2 = 3 027 238 + 1;
  • 3 027 238 ÷ 2 = 1 513 619 + 0;
  • 1 513 619 ÷ 2 = 756 809 + 1;
  • 756 809 ÷ 2 = 378 404 + 1;
  • 378 404 ÷ 2 = 189 202 + 0;
  • 189 202 ÷ 2 = 94 601 + 0;
  • 94 601 ÷ 2 = 47 300 + 1;
  • 47 300 ÷ 2 = 23 650 + 0;
  • 23 650 ÷ 2 = 11 825 + 0;
  • 11 825 ÷ 2 = 5 912 + 1;
  • 5 912 ÷ 2 = 2 956 + 0;
  • 2 956 ÷ 2 = 1 478 + 0;
  • 1 478 ÷ 2 = 739 + 0;
  • 739 ÷ 2 = 369 + 1;
  • 369 ÷ 2 = 184 + 1;
  • 184 ÷ 2 = 92 + 0;
  • 92 ÷ 2 = 46 + 0;
  • 46 ÷ 2 = 23 + 0;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 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.

12 697 160 277 502(10) = 1011 1000 1100 0100 1001 1011 1010 0101 1101 1111 1110(2)


4. 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) 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, 44,

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:


12 697 160 277 502(10) = 0000 0000 0000 0000 0000 1011 1000 1100 0100 1001 1011 1010 0101 1101 1111 1110

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...


-12 697 160 277 502(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-12 697 160 277 502(10) = 1000 0000 0000 0000 0000 1011 1000 1100 0100 1001 1011 1010 0101 1101 1111 1110

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

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How to convert signed base 10 integers in decimal 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