Signed: Integer ↗ Binary: -10 654 324 631 552 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 -10 654 324 631 552(10)
converted and written as a signed binary (base 2) = ?

1. Start with the positive version of the number:

|-10 654 324 631 552| = 10 654 324 631 552

2. 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;
  • 10 654 324 631 552 ÷ 2 = 5 327 162 315 776 + 0;
  • 5 327 162 315 776 ÷ 2 = 2 663 581 157 888 + 0;
  • 2 663 581 157 888 ÷ 2 = 1 331 790 578 944 + 0;
  • 1 331 790 578 944 ÷ 2 = 665 895 289 472 + 0;
  • 665 895 289 472 ÷ 2 = 332 947 644 736 + 0;
  • 332 947 644 736 ÷ 2 = 166 473 822 368 + 0;
  • 166 473 822 368 ÷ 2 = 83 236 911 184 + 0;
  • 83 236 911 184 ÷ 2 = 41 618 455 592 + 0;
  • 41 618 455 592 ÷ 2 = 20 809 227 796 + 0;
  • 20 809 227 796 ÷ 2 = 10 404 613 898 + 0;
  • 10 404 613 898 ÷ 2 = 5 202 306 949 + 0;
  • 5 202 306 949 ÷ 2 = 2 601 153 474 + 1;
  • 2 601 153 474 ÷ 2 = 1 300 576 737 + 0;
  • 1 300 576 737 ÷ 2 = 650 288 368 + 1;
  • 650 288 368 ÷ 2 = 325 144 184 + 0;
  • 325 144 184 ÷ 2 = 162 572 092 + 0;
  • 162 572 092 ÷ 2 = 81 286 046 + 0;
  • 81 286 046 ÷ 2 = 40 643 023 + 0;
  • 40 643 023 ÷ 2 = 20 321 511 + 1;
  • 20 321 511 ÷ 2 = 10 160 755 + 1;
  • 10 160 755 ÷ 2 = 5 080 377 + 1;
  • 5 080 377 ÷ 2 = 2 540 188 + 1;
  • 2 540 188 ÷ 2 = 1 270 094 + 0;
  • 1 270 094 ÷ 2 = 635 047 + 0;
  • 635 047 ÷ 2 = 317 523 + 1;
  • 317 523 ÷ 2 = 158 761 + 1;
  • 158 761 ÷ 2 = 79 380 + 1;
  • 79 380 ÷ 2 = 39 690 + 0;
  • 39 690 ÷ 2 = 19 845 + 0;
  • 19 845 ÷ 2 = 9 922 + 1;
  • 9 922 ÷ 2 = 4 961 + 0;
  • 4 961 ÷ 2 = 2 480 + 1;
  • 2 480 ÷ 2 = 1 240 + 0;
  • 1 240 ÷ 2 = 620 + 0;
  • 620 ÷ 2 = 310 + 0;
  • 310 ÷ 2 = 155 + 0;
  • 155 ÷ 2 = 77 + 1;
  • 77 ÷ 2 = 38 + 1;
  • 38 ÷ 2 = 19 + 0;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.


10 654 324 631 552(10) = 1001 1011 0000 1010 0111 0011 1100 0010 1000 0000 0000(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 44.


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, 44,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)


=== is: 64.


5. 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:


10 654 324 631 552(10) = 0000 0000 0000 0000 0000 1001 1011 0000 1010 0111 0011 1100 0010 1000 0000 0000


6. Get the negative integer number representation:

To get the negative integer number representation on 64 bits (8 Bytes),


... change the first bit (the leftmost), from 0 to 1...


Number -10 654 324 631 552(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-10 654 324 631 552(10) = 1000 0000 0000 0000 0000 1001 1011 0000 1010 0111 0011 1100 0010 1000 0000 0000

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

The latest signed integer numbers (that are written in decimal system, in base ten) converted and written as signed binary numbers

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