Signed: Integer ↗ Binary: 9 223 372 036 854 775 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 9 223 372 036 854 775(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;
  • 9 223 372 036 854 775 ÷ 2 = 4 611 686 018 427 387 + 1;
  • 4 611 686 018 427 387 ÷ 2 = 2 305 843 009 213 693 + 1;
  • 2 305 843 009 213 693 ÷ 2 = 1 152 921 504 606 846 + 1;
  • 1 152 921 504 606 846 ÷ 2 = 576 460 752 303 423 + 0;
  • 576 460 752 303 423 ÷ 2 = 288 230 376 151 711 + 1;
  • 288 230 376 151 711 ÷ 2 = 144 115 188 075 855 + 1;
  • 144 115 188 075 855 ÷ 2 = 72 057 594 037 927 + 1;
  • 72 057 594 037 927 ÷ 2 = 36 028 797 018 963 + 1;
  • 36 028 797 018 963 ÷ 2 = 18 014 398 509 481 + 1;
  • 18 014 398 509 481 ÷ 2 = 9 007 199 254 740 + 1;
  • 9 007 199 254 740 ÷ 2 = 4 503 599 627 370 + 0;
  • 4 503 599 627 370 ÷ 2 = 2 251 799 813 685 + 0;
  • 2 251 799 813 685 ÷ 2 = 1 125 899 906 842 + 1;
  • 1 125 899 906 842 ÷ 2 = 562 949 953 421 + 0;
  • 562 949 953 421 ÷ 2 = 281 474 976 710 + 1;
  • 281 474 976 710 ÷ 2 = 140 737 488 355 + 0;
  • 140 737 488 355 ÷ 2 = 70 368 744 177 + 1;
  • 70 368 744 177 ÷ 2 = 35 184 372 088 + 1;
  • 35 184 372 088 ÷ 2 = 17 592 186 044 + 0;
  • 17 592 186 044 ÷ 2 = 8 796 093 022 + 0;
  • 8 796 093 022 ÷ 2 = 4 398 046 511 + 0;
  • 4 398 046 511 ÷ 2 = 2 199 023 255 + 1;
  • 2 199 023 255 ÷ 2 = 1 099 511 627 + 1;
  • 1 099 511 627 ÷ 2 = 549 755 813 + 1;
  • 549 755 813 ÷ 2 = 274 877 906 + 1;
  • 274 877 906 ÷ 2 = 137 438 953 + 0;
  • 137 438 953 ÷ 2 = 68 719 476 + 1;
  • 68 719 476 ÷ 2 = 34 359 738 + 0;
  • 34 359 738 ÷ 2 = 17 179 869 + 0;
  • 17 179 869 ÷ 2 = 8 589 934 + 1;
  • 8 589 934 ÷ 2 = 4 294 967 + 0;
  • 4 294 967 ÷ 2 = 2 147 483 + 1;
  • 2 147 483 ÷ 2 = 1 073 741 + 1;
  • 1 073 741 ÷ 2 = 536 870 + 1;
  • 536 870 ÷ 2 = 268 435 + 0;
  • 268 435 ÷ 2 = 134 217 + 1;
  • 134 217 ÷ 2 = 67 108 + 1;
  • 67 108 ÷ 2 = 33 554 + 0;
  • 33 554 ÷ 2 = 16 777 + 0;
  • 16 777 ÷ 2 = 8 388 + 1;
  • 8 388 ÷ 2 = 4 194 + 0;
  • 4 194 ÷ 2 = 2 097 + 0;
  • 2 097 ÷ 2 = 1 048 + 1;
  • 1 048 ÷ 2 = 524 + 0;
  • 524 ÷ 2 = 262 + 0;
  • 262 ÷ 2 = 131 + 0;
  • 131 ÷ 2 = 65 + 1;
  • 65 ÷ 2 = 32 + 1;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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.


9 223 372 036 854 775(10) = 10 0000 1100 0100 1001 1011 1010 0101 1110 0011 0101 0011 1111 0111(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 54.

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, 54,

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 9 223 372 036 854 775(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

9 223 372 036 854 775(10) = 0000 0000 0010 0000 1100 0100 1001 1011 1010 0101 1110 0011 0101 0011 1111 0111

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

More operations on signed integer numbers:

» Signed integer number 9 223 372 036 854 774 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 9 223 372 036 854 776 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