Signed: Integer ↗ Binary: 139 948 407 982 510 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 139 948 407 982 510(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;
  • 139 948 407 982 510 ÷ 2 = 69 974 203 991 255 + 0;
  • 69 974 203 991 255 ÷ 2 = 34 987 101 995 627 + 1;
  • 34 987 101 995 627 ÷ 2 = 17 493 550 997 813 + 1;
  • 17 493 550 997 813 ÷ 2 = 8 746 775 498 906 + 1;
  • 8 746 775 498 906 ÷ 2 = 4 373 387 749 453 + 0;
  • 4 373 387 749 453 ÷ 2 = 2 186 693 874 726 + 1;
  • 2 186 693 874 726 ÷ 2 = 1 093 346 937 363 + 0;
  • 1 093 346 937 363 ÷ 2 = 546 673 468 681 + 1;
  • 546 673 468 681 ÷ 2 = 273 336 734 340 + 1;
  • 273 336 734 340 ÷ 2 = 136 668 367 170 + 0;
  • 136 668 367 170 ÷ 2 = 68 334 183 585 + 0;
  • 68 334 183 585 ÷ 2 = 34 167 091 792 + 1;
  • 34 167 091 792 ÷ 2 = 17 083 545 896 + 0;
  • 17 083 545 896 ÷ 2 = 8 541 772 948 + 0;
  • 8 541 772 948 ÷ 2 = 4 270 886 474 + 0;
  • 4 270 886 474 ÷ 2 = 2 135 443 237 + 0;
  • 2 135 443 237 ÷ 2 = 1 067 721 618 + 1;
  • 1 067 721 618 ÷ 2 = 533 860 809 + 0;
  • 533 860 809 ÷ 2 = 266 930 404 + 1;
  • 266 930 404 ÷ 2 = 133 465 202 + 0;
  • 133 465 202 ÷ 2 = 66 732 601 + 0;
  • 66 732 601 ÷ 2 = 33 366 300 + 1;
  • 33 366 300 ÷ 2 = 16 683 150 + 0;
  • 16 683 150 ÷ 2 = 8 341 575 + 0;
  • 8 341 575 ÷ 2 = 4 170 787 + 1;
  • 4 170 787 ÷ 2 = 2 085 393 + 1;
  • 2 085 393 ÷ 2 = 1 042 696 + 1;
  • 1 042 696 ÷ 2 = 521 348 + 0;
  • 521 348 ÷ 2 = 260 674 + 0;
  • 260 674 ÷ 2 = 130 337 + 0;
  • 130 337 ÷ 2 = 65 168 + 1;
  • 65 168 ÷ 2 = 32 584 + 0;
  • 32 584 ÷ 2 = 16 292 + 0;
  • 16 292 ÷ 2 = 8 146 + 0;
  • 8 146 ÷ 2 = 4 073 + 0;
  • 4 073 ÷ 2 = 2 036 + 1;
  • 2 036 ÷ 2 = 1 018 + 0;
  • 1 018 ÷ 2 = 509 + 0;
  • 509 ÷ 2 = 254 + 1;
  • 254 ÷ 2 = 127 + 0;
  • 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.


139 948 407 982 510(10) = 111 1111 0100 1000 0100 0111 0010 0101 0000 1001 1010 1110(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 47.

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, 47,

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 139 948 407 982 510(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

139 948 407 982 510(10) = 0000 0000 0000 0000 0111 1111 0100 1000 0100 0111 0010 0101 0000 1001 1010 1110

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

More operations on signed integer numbers:

» Signed integer number 139 948 407 982 509 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 139 948 407 982 511 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