Convert 1 011 000 000 000 750 to a Signed Binary (Base 2)

How to convert 1 011 000 000 000 750(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 1 011 000 000 000 750 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;
  • 1 011 000 000 000 750 ÷ 2 = 505 500 000 000 375 + 0;
  • 505 500 000 000 375 ÷ 2 = 252 750 000 000 187 + 1;
  • 252 750 000 000 187 ÷ 2 = 126 375 000 000 093 + 1;
  • 126 375 000 000 093 ÷ 2 = 63 187 500 000 046 + 1;
  • 63 187 500 000 046 ÷ 2 = 31 593 750 000 023 + 0;
  • 31 593 750 000 023 ÷ 2 = 15 796 875 000 011 + 1;
  • 15 796 875 000 011 ÷ 2 = 7 898 437 500 005 + 1;
  • 7 898 437 500 005 ÷ 2 = 3 949 218 750 002 + 1;
  • 3 949 218 750 002 ÷ 2 = 1 974 609 375 001 + 0;
  • 1 974 609 375 001 ÷ 2 = 987 304 687 500 + 1;
  • 987 304 687 500 ÷ 2 = 493 652 343 750 + 0;
  • 493 652 343 750 ÷ 2 = 246 826 171 875 + 0;
  • 246 826 171 875 ÷ 2 = 123 413 085 937 + 1;
  • 123 413 085 937 ÷ 2 = 61 706 542 968 + 1;
  • 61 706 542 968 ÷ 2 = 30 853 271 484 + 0;
  • 30 853 271 484 ÷ 2 = 15 426 635 742 + 0;
  • 15 426 635 742 ÷ 2 = 7 713 317 871 + 0;
  • 7 713 317 871 ÷ 2 = 3 856 658 935 + 1;
  • 3 856 658 935 ÷ 2 = 1 928 329 467 + 1;
  • 1 928 329 467 ÷ 2 = 964 164 733 + 1;
  • 964 164 733 ÷ 2 = 482 082 366 + 1;
  • 482 082 366 ÷ 2 = 241 041 183 + 0;
  • 241 041 183 ÷ 2 = 120 520 591 + 1;
  • 120 520 591 ÷ 2 = 60 260 295 + 1;
  • 60 260 295 ÷ 2 = 30 130 147 + 1;
  • 30 130 147 ÷ 2 = 15 065 073 + 1;
  • 15 065 073 ÷ 2 = 7 532 536 + 1;
  • 7 532 536 ÷ 2 = 3 766 268 + 0;
  • 3 766 268 ÷ 2 = 1 883 134 + 0;
  • 1 883 134 ÷ 2 = 941 567 + 0;
  • 941 567 ÷ 2 = 470 783 + 1;
  • 470 783 ÷ 2 = 235 391 + 1;
  • 235 391 ÷ 2 = 117 695 + 1;
  • 117 695 ÷ 2 = 58 847 + 1;
  • 58 847 ÷ 2 = 29 423 + 1;
  • 29 423 ÷ 2 = 14 711 + 1;
  • 14 711 ÷ 2 = 7 355 + 1;
  • 7 355 ÷ 2 = 3 677 + 1;
  • 3 677 ÷ 2 = 1 838 + 1;
  • 1 838 ÷ 2 = 919 + 0;
  • 919 ÷ 2 = 459 + 1;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.

1 011 000 000 000 750(10) = 11 1001 0111 0111 1111 1100 0111 1101 1110 0011 0010 1110 1110(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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, 50,

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:


1 011 000 000 000 750(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 011 000 000 000 750(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 0111 1101 1110 0011 0010 1110 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