Signed: Integer ↗ Binary: 4 288 675 909 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 4 288 675 909(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;
  • 4 288 675 909 ÷ 2 = 2 144 337 954 + 1;
  • 2 144 337 954 ÷ 2 = 1 072 168 977 + 0;
  • 1 072 168 977 ÷ 2 = 536 084 488 + 1;
  • 536 084 488 ÷ 2 = 268 042 244 + 0;
  • 268 042 244 ÷ 2 = 134 021 122 + 0;
  • 134 021 122 ÷ 2 = 67 010 561 + 0;
  • 67 010 561 ÷ 2 = 33 505 280 + 1;
  • 33 505 280 ÷ 2 = 16 752 640 + 0;
  • 16 752 640 ÷ 2 = 8 376 320 + 0;
  • 8 376 320 ÷ 2 = 4 188 160 + 0;
  • 4 188 160 ÷ 2 = 2 094 080 + 0;
  • 2 094 080 ÷ 2 = 1 047 040 + 0;
  • 1 047 040 ÷ 2 = 523 520 + 0;
  • 523 520 ÷ 2 = 261 760 + 0;
  • 261 760 ÷ 2 = 130 880 + 0;
  • 130 880 ÷ 2 = 65 440 + 0;
  • 65 440 ÷ 2 = 32 720 + 0;
  • 32 720 ÷ 2 = 16 360 + 0;
  • 16 360 ÷ 2 = 8 180 + 0;
  • 8 180 ÷ 2 = 4 090 + 0;
  • 4 090 ÷ 2 = 2 045 + 0;
  • 2 045 ÷ 2 = 1 022 + 1;
  • 1 022 ÷ 2 = 511 + 0;
  • 511 ÷ 2 = 255 + 1;
  • 255 ÷ 2 = 127 + 1;
  • 127 ÷ 2 = 63 + 1;
  • 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.


4 288 675 909(10) = 1111 1111 1010 0000 0000 0000 0100 0101(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 32.

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, 32,

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 4 288 675 909(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

4 288 675 909(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1111 1111 1010 0000 0000 0000 0100 0101

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

More operations on signed integer numbers:

» Signed integer number 4 288 675 908 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 4 288 675 910 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