Convert 1 110 001 100 001 387 to a Signed Binary (Base 2)

How to convert 1 110 001 100 001 387(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 1 110 001 100 001 387 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;
  • 1 110 001 100 001 387 ÷ 2 = 555 000 550 000 693 + 1;
  • 555 000 550 000 693 ÷ 2 = 277 500 275 000 346 + 1;
  • 277 500 275 000 346 ÷ 2 = 138 750 137 500 173 + 0;
  • 138 750 137 500 173 ÷ 2 = 69 375 068 750 086 + 1;
  • 69 375 068 750 086 ÷ 2 = 34 687 534 375 043 + 0;
  • 34 687 534 375 043 ÷ 2 = 17 343 767 187 521 + 1;
  • 17 343 767 187 521 ÷ 2 = 8 671 883 593 760 + 1;
  • 8 671 883 593 760 ÷ 2 = 4 335 941 796 880 + 0;
  • 4 335 941 796 880 ÷ 2 = 2 167 970 898 440 + 0;
  • 2 167 970 898 440 ÷ 2 = 1 083 985 449 220 + 0;
  • 1 083 985 449 220 ÷ 2 = 541 992 724 610 + 0;
  • 541 992 724 610 ÷ 2 = 270 996 362 305 + 0;
  • 270 996 362 305 ÷ 2 = 135 498 181 152 + 1;
  • 135 498 181 152 ÷ 2 = 67 749 090 576 + 0;
  • 67 749 090 576 ÷ 2 = 33 874 545 288 + 0;
  • 33 874 545 288 ÷ 2 = 16 937 272 644 + 0;
  • 16 937 272 644 ÷ 2 = 8 468 636 322 + 0;
  • 8 468 636 322 ÷ 2 = 4 234 318 161 + 0;
  • 4 234 318 161 ÷ 2 = 2 117 159 080 + 1;
  • 2 117 159 080 ÷ 2 = 1 058 579 540 + 0;
  • 1 058 579 540 ÷ 2 = 529 289 770 + 0;
  • 529 289 770 ÷ 2 = 264 644 885 + 0;
  • 264 644 885 ÷ 2 = 132 322 442 + 1;
  • 132 322 442 ÷ 2 = 66 161 221 + 0;
  • 66 161 221 ÷ 2 = 33 080 610 + 1;
  • 33 080 610 ÷ 2 = 16 540 305 + 0;
  • 16 540 305 ÷ 2 = 8 270 152 + 1;
  • 8 270 152 ÷ 2 = 4 135 076 + 0;
  • 4 135 076 ÷ 2 = 2 067 538 + 0;
  • 2 067 538 ÷ 2 = 1 033 769 + 0;
  • 1 033 769 ÷ 2 = 516 884 + 1;
  • 516 884 ÷ 2 = 258 442 + 0;
  • 258 442 ÷ 2 = 129 221 + 0;
  • 129 221 ÷ 2 = 64 610 + 1;
  • 64 610 ÷ 2 = 32 305 + 0;
  • 32 305 ÷ 2 = 16 152 + 1;
  • 16 152 ÷ 2 = 8 076 + 0;
  • 8 076 ÷ 2 = 4 038 + 0;
  • 4 038 ÷ 2 = 2 019 + 0;
  • 2 019 ÷ 2 = 1 009 + 1;
  • 1 009 ÷ 2 = 504 + 1;
  • 504 ÷ 2 = 252 + 0;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.

1 110 001 100 001 387(10) = 11 1111 0001 1000 1010 0100 0101 0100 0100 0001 0000 0110 1011(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:


1 110 001 100 001 387(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 110 001 100 001 387(10) = 0000 0000 0000 0011 1111 0001 1000 1010 0100 0101 0100 0100 0001 0000 0110 1011

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