Signed: Integer ↗ Binary: 100 111 000 008 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number 100 111 000 008(10)
converted and written as a signed binary (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 100 111 000 008 ÷ 2 = 50 055 500 004 + 0;
  • 50 055 500 004 ÷ 2 = 25 027 750 002 + 0;
  • 25 027 750 002 ÷ 2 = 12 513 875 001 + 0;
  • 12 513 875 001 ÷ 2 = 6 256 937 500 + 1;
  • 6 256 937 500 ÷ 2 = 3 128 468 750 + 0;
  • 3 128 468 750 ÷ 2 = 1 564 234 375 + 0;
  • 1 564 234 375 ÷ 2 = 782 117 187 + 1;
  • 782 117 187 ÷ 2 = 391 058 593 + 1;
  • 391 058 593 ÷ 2 = 195 529 296 + 1;
  • 195 529 296 ÷ 2 = 97 764 648 + 0;
  • 97 764 648 ÷ 2 = 48 882 324 + 0;
  • 48 882 324 ÷ 2 = 24 441 162 + 0;
  • 24 441 162 ÷ 2 = 12 220 581 + 0;
  • 12 220 581 ÷ 2 = 6 110 290 + 1;
  • 6 110 290 ÷ 2 = 3 055 145 + 0;
  • 3 055 145 ÷ 2 = 1 527 572 + 1;
  • 1 527 572 ÷ 2 = 763 786 + 0;
  • 763 786 ÷ 2 = 381 893 + 0;
  • 381 893 ÷ 2 = 190 946 + 1;
  • 190 946 ÷ 2 = 95 473 + 0;
  • 95 473 ÷ 2 = 47 736 + 1;
  • 47 736 ÷ 2 = 23 868 + 0;
  • 23 868 ÷ 2 = 11 934 + 0;
  • 11 934 ÷ 2 = 5 967 + 0;
  • 5 967 ÷ 2 = 2 983 + 1;
  • 2 983 ÷ 2 = 1 491 + 1;
  • 1 491 ÷ 2 = 745 + 1;
  • 745 ÷ 2 = 372 + 1;
  • 372 ÷ 2 = 186 + 0;
  • 186 ÷ 2 = 93 + 0;
  • 93 ÷ 2 = 46 + 1;
  • 46 ÷ 2 = 23 + 0;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 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.


100 111 000 008(10) = 1 0111 0100 1111 0001 0100 1010 0001 1100 1000(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 37.

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, 37,

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:


Number 100 111 000 008(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

100 111 000 008(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1111 0001 0100 1010 0001 1100 1000

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

More operations on signed integer numbers:

» Signed integer number 100 111 000 007 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 100 111 000 009 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

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How to convert signed integers from decimal system 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