Integer to Signed Binary: Number 472 115 111 738 Converted and Written as a Signed Binary. Base Ten Decimal System Conversion

Integer number 472 115 111 738(10) written as a signed binary number

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;
  • 472 115 111 738 ÷ 2 = 236 057 555 869 + 0;
  • 236 057 555 869 ÷ 2 = 118 028 777 934 + 1;
  • 118 028 777 934 ÷ 2 = 59 014 388 967 + 0;
  • 59 014 388 967 ÷ 2 = 29 507 194 483 + 1;
  • 29 507 194 483 ÷ 2 = 14 753 597 241 + 1;
  • 14 753 597 241 ÷ 2 = 7 376 798 620 + 1;
  • 7 376 798 620 ÷ 2 = 3 688 399 310 + 0;
  • 3 688 399 310 ÷ 2 = 1 844 199 655 + 0;
  • 1 844 199 655 ÷ 2 = 922 099 827 + 1;
  • 922 099 827 ÷ 2 = 461 049 913 + 1;
  • 461 049 913 ÷ 2 = 230 524 956 + 1;
  • 230 524 956 ÷ 2 = 115 262 478 + 0;
  • 115 262 478 ÷ 2 = 57 631 239 + 0;
  • 57 631 239 ÷ 2 = 28 815 619 + 1;
  • 28 815 619 ÷ 2 = 14 407 809 + 1;
  • 14 407 809 ÷ 2 = 7 203 904 + 1;
  • 7 203 904 ÷ 2 = 3 601 952 + 0;
  • 3 601 952 ÷ 2 = 1 800 976 + 0;
  • 1 800 976 ÷ 2 = 900 488 + 0;
  • 900 488 ÷ 2 = 450 244 + 0;
  • 450 244 ÷ 2 = 225 122 + 0;
  • 225 122 ÷ 2 = 112 561 + 0;
  • 112 561 ÷ 2 = 56 280 + 1;
  • 56 280 ÷ 2 = 28 140 + 0;
  • 28 140 ÷ 2 = 14 070 + 0;
  • 14 070 ÷ 2 = 7 035 + 0;
  • 7 035 ÷ 2 = 3 517 + 1;
  • 3 517 ÷ 2 = 1 758 + 1;
  • 1 758 ÷ 2 = 879 + 0;
  • 879 ÷ 2 = 439 + 1;
  • 439 ÷ 2 = 219 + 1;
  • 219 ÷ 2 = 109 + 1;
  • 109 ÷ 2 = 54 + 1;
  • 54 ÷ 2 = 27 + 0;
  • 27 ÷ 2 = 13 + 1;
  • 13 ÷ 2 = 6 + 1;
  • 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.

472 115 111 738(10) = 110 1101 1110 1100 0100 0000 1110 0111 0011 1010(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 39.

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, 39,

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 472 115 111 738(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

472 115 111 738(10) = 0000 0000 0000 0000 0000 0000 0110 1101 1110 1100 0100 0000 1110 0111 0011 1010

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

» More ops: Integer number 472 115 111 783 converted and written as a signed binary number

» New: All the Calculations Performed by Our Visitors: Integer numbers converted and written as signed binary numbers. Data organized on a Monthly Basis

» Month 01, 2025 [January]: Integer Numbers Converted and Written as Signed Binary. Monthly Calculations performed during the month of: January - by our visitors

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