Signed: Integer ↗ Binary: 1 010 000 010 110 085 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 1 010 000 010 110 085(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;
  • 1 010 000 010 110 085 ÷ 2 = 505 000 005 055 042 + 1;
  • 505 000 005 055 042 ÷ 2 = 252 500 002 527 521 + 0;
  • 252 500 002 527 521 ÷ 2 = 126 250 001 263 760 + 1;
  • 126 250 001 263 760 ÷ 2 = 63 125 000 631 880 + 0;
  • 63 125 000 631 880 ÷ 2 = 31 562 500 315 940 + 0;
  • 31 562 500 315 940 ÷ 2 = 15 781 250 157 970 + 0;
  • 15 781 250 157 970 ÷ 2 = 7 890 625 078 985 + 0;
  • 7 890 625 078 985 ÷ 2 = 3 945 312 539 492 + 1;
  • 3 945 312 539 492 ÷ 2 = 1 972 656 269 746 + 0;
  • 1 972 656 269 746 ÷ 2 = 986 328 134 873 + 0;
  • 986 328 134 873 ÷ 2 = 493 164 067 436 + 1;
  • 493 164 067 436 ÷ 2 = 246 582 033 718 + 0;
  • 246 582 033 718 ÷ 2 = 123 291 016 859 + 0;
  • 123 291 016 859 ÷ 2 = 61 645 508 429 + 1;
  • 61 645 508 429 ÷ 2 = 30 822 754 214 + 1;
  • 30 822 754 214 ÷ 2 = 15 411 377 107 + 0;
  • 15 411 377 107 ÷ 2 = 7 705 688 553 + 1;
  • 7 705 688 553 ÷ 2 = 3 852 844 276 + 1;
  • 3 852 844 276 ÷ 2 = 1 926 422 138 + 0;
  • 1 926 422 138 ÷ 2 = 963 211 069 + 0;
  • 963 211 069 ÷ 2 = 481 605 534 + 1;
  • 481 605 534 ÷ 2 = 240 802 767 + 0;
  • 240 802 767 ÷ 2 = 120 401 383 + 1;
  • 120 401 383 ÷ 2 = 60 200 691 + 1;
  • 60 200 691 ÷ 2 = 30 100 345 + 1;
  • 30 100 345 ÷ 2 = 15 050 172 + 1;
  • 15 050 172 ÷ 2 = 7 525 086 + 0;
  • 7 525 086 ÷ 2 = 3 762 543 + 0;
  • 3 762 543 ÷ 2 = 1 881 271 + 1;
  • 1 881 271 ÷ 2 = 940 635 + 1;
  • 940 635 ÷ 2 = 470 317 + 1;
  • 470 317 ÷ 2 = 235 158 + 1;
  • 235 158 ÷ 2 = 117 579 + 0;
  • 117 579 ÷ 2 = 58 789 + 1;
  • 58 789 ÷ 2 = 29 394 + 1;
  • 29 394 ÷ 2 = 14 697 + 0;
  • 14 697 ÷ 2 = 7 348 + 1;
  • 7 348 ÷ 2 = 3 674 + 0;
  • 3 674 ÷ 2 = 1 837 + 0;
  • 1 837 ÷ 2 = 918 + 1;
  • 918 ÷ 2 = 459 + 0;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 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.


1 010 000 010 110 085(10) = 11 1001 0110 1001 0110 1111 0011 1101 0011 0110 0100 1000 0101(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 50.

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, 50,

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 1 010 000 010 110 085(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 010 000 010 110 085(10) = 0000 0000 0000 0011 1001 0110 1001 0110 1111 0011 1101 0011 0110 0100 1000 0101

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

More operations on signed integer numbers:

» Signed integer number 1 010 000 010 110 084 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 1 010 000 010 110 086 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