Convert 110 100 001 111 337 to a Signed Binary (Base 2)

How to convert 110 100 001 111 337(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 110 100 001 111 337 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;
  • 110 100 001 111 337 ÷ 2 = 55 050 000 555 668 + 1;
  • 55 050 000 555 668 ÷ 2 = 27 525 000 277 834 + 0;
  • 27 525 000 277 834 ÷ 2 = 13 762 500 138 917 + 0;
  • 13 762 500 138 917 ÷ 2 = 6 881 250 069 458 + 1;
  • 6 881 250 069 458 ÷ 2 = 3 440 625 034 729 + 0;
  • 3 440 625 034 729 ÷ 2 = 1 720 312 517 364 + 1;
  • 1 720 312 517 364 ÷ 2 = 860 156 258 682 + 0;
  • 860 156 258 682 ÷ 2 = 430 078 129 341 + 0;
  • 430 078 129 341 ÷ 2 = 215 039 064 670 + 1;
  • 215 039 064 670 ÷ 2 = 107 519 532 335 + 0;
  • 107 519 532 335 ÷ 2 = 53 759 766 167 + 1;
  • 53 759 766 167 ÷ 2 = 26 879 883 083 + 1;
  • 26 879 883 083 ÷ 2 = 13 439 941 541 + 1;
  • 13 439 941 541 ÷ 2 = 6 719 970 770 + 1;
  • 6 719 970 770 ÷ 2 = 3 359 985 385 + 0;
  • 3 359 985 385 ÷ 2 = 1 679 992 692 + 1;
  • 1 679 992 692 ÷ 2 = 839 996 346 + 0;
  • 839 996 346 ÷ 2 = 419 998 173 + 0;
  • 419 998 173 ÷ 2 = 209 999 086 + 1;
  • 209 999 086 ÷ 2 = 104 999 543 + 0;
  • 104 999 543 ÷ 2 = 52 499 771 + 1;
  • 52 499 771 ÷ 2 = 26 249 885 + 1;
  • 26 249 885 ÷ 2 = 13 124 942 + 1;
  • 13 124 942 ÷ 2 = 6 562 471 + 0;
  • 6 562 471 ÷ 2 = 3 281 235 + 1;
  • 3 281 235 ÷ 2 = 1 640 617 + 1;
  • 1 640 617 ÷ 2 = 820 308 + 1;
  • 820 308 ÷ 2 = 410 154 + 0;
  • 410 154 ÷ 2 = 205 077 + 0;
  • 205 077 ÷ 2 = 102 538 + 1;
  • 102 538 ÷ 2 = 51 269 + 0;
  • 51 269 ÷ 2 = 25 634 + 1;
  • 25 634 ÷ 2 = 12 817 + 0;
  • 12 817 ÷ 2 = 6 408 + 1;
  • 6 408 ÷ 2 = 3 204 + 0;
  • 3 204 ÷ 2 = 1 602 + 0;
  • 1 602 ÷ 2 = 801 + 0;
  • 801 ÷ 2 = 400 + 1;
  • 400 ÷ 2 = 200 + 0;
  • 200 ÷ 2 = 100 + 0;
  • 100 ÷ 2 = 50 + 0;
  • 50 ÷ 2 = 25 + 0;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 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.

110 100 001 111 337(10) = 110 0100 0010 0010 1010 0111 0111 0100 1011 1101 0010 1001(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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, 47,

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:


110 100 001 111 337(10) Base 10 integer number converted and written as a signed binary code (in base 2):

110 100 001 111 337(10) = 0000 0000 0000 0000 0110 0100 0010 0010 1010 0111 0111 0100 1011 1101 0010 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