Convert 11 111 011 101 097 to a Signed Binary (Base 2)

How to convert 11 111 011 101 097(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 11 111 011 101 097 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. 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;
  • 11 111 011 101 097 ÷ 2 = 5 555 505 550 548 + 1;
  • 5 555 505 550 548 ÷ 2 = 2 777 752 775 274 + 0;
  • 2 777 752 775 274 ÷ 2 = 1 388 876 387 637 + 0;
  • 1 388 876 387 637 ÷ 2 = 694 438 193 818 + 1;
  • 694 438 193 818 ÷ 2 = 347 219 096 909 + 0;
  • 347 219 096 909 ÷ 2 = 173 609 548 454 + 1;
  • 173 609 548 454 ÷ 2 = 86 804 774 227 + 0;
  • 86 804 774 227 ÷ 2 = 43 402 387 113 + 1;
  • 43 402 387 113 ÷ 2 = 21 701 193 556 + 1;
  • 21 701 193 556 ÷ 2 = 10 850 596 778 + 0;
  • 10 850 596 778 ÷ 2 = 5 425 298 389 + 0;
  • 5 425 298 389 ÷ 2 = 2 712 649 194 + 1;
  • 2 712 649 194 ÷ 2 = 1 356 324 597 + 0;
  • 1 356 324 597 ÷ 2 = 678 162 298 + 1;
  • 678 162 298 ÷ 2 = 339 081 149 + 0;
  • 339 081 149 ÷ 2 = 169 540 574 + 1;
  • 169 540 574 ÷ 2 = 84 770 287 + 0;
  • 84 770 287 ÷ 2 = 42 385 143 + 1;
  • 42 385 143 ÷ 2 = 21 192 571 + 1;
  • 21 192 571 ÷ 2 = 10 596 285 + 1;
  • 10 596 285 ÷ 2 = 5 298 142 + 1;
  • 5 298 142 ÷ 2 = 2 649 071 + 0;
  • 2 649 071 ÷ 2 = 1 324 535 + 1;
  • 1 324 535 ÷ 2 = 662 267 + 1;
  • 662 267 ÷ 2 = 331 133 + 1;
  • 331 133 ÷ 2 = 165 566 + 1;
  • 165 566 ÷ 2 = 82 783 + 0;
  • 82 783 ÷ 2 = 41 391 + 1;
  • 41 391 ÷ 2 = 20 695 + 1;
  • 20 695 ÷ 2 = 10 347 + 1;
  • 10 347 ÷ 2 = 5 173 + 1;
  • 5 173 ÷ 2 = 2 586 + 1;
  • 2 586 ÷ 2 = 1 293 + 0;
  • 1 293 ÷ 2 = 646 + 1;
  • 646 ÷ 2 = 323 + 0;
  • 323 ÷ 2 = 161 + 1;
  • 161 ÷ 2 = 80 + 1;
  • 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.

11 111 011 101 097(10) = 1010 0001 1010 1111 1011 1101 1110 1010 1001 1010 1001(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) 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.


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:


11 111 011 101 097(10) Base 10 integer number converted and written as a signed binary code (in base 2):

11 111 011 101 097(10) = 0000 0000 0000 0000 0000 1010 0001 1010 1111 1011 1101 1110 1010 1001 1010 1001

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