Integer to Signed Binary: Number 1 111 111 101 111 083 Converted and Written as a Signed Binary. Base Ten Decimal System Conversion

Integer number 1 111 111 101 111 083(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;
  • 1 111 111 101 111 083 ÷ 2 = 555 555 550 555 541 + 1;
  • 555 555 550 555 541 ÷ 2 = 277 777 775 277 770 + 1;
  • 277 777 775 277 770 ÷ 2 = 138 888 887 638 885 + 0;
  • 138 888 887 638 885 ÷ 2 = 69 444 443 819 442 + 1;
  • 69 444 443 819 442 ÷ 2 = 34 722 221 909 721 + 0;
  • 34 722 221 909 721 ÷ 2 = 17 361 110 954 860 + 1;
  • 17 361 110 954 860 ÷ 2 = 8 680 555 477 430 + 0;
  • 8 680 555 477 430 ÷ 2 = 4 340 277 738 715 + 0;
  • 4 340 277 738 715 ÷ 2 = 2 170 138 869 357 + 1;
  • 2 170 138 869 357 ÷ 2 = 1 085 069 434 678 + 1;
  • 1 085 069 434 678 ÷ 2 = 542 534 717 339 + 0;
  • 542 534 717 339 ÷ 2 = 271 267 358 669 + 1;
  • 271 267 358 669 ÷ 2 = 135 633 679 334 + 1;
  • 135 633 679 334 ÷ 2 = 67 816 839 667 + 0;
  • 67 816 839 667 ÷ 2 = 33 908 419 833 + 1;
  • 33 908 419 833 ÷ 2 = 16 954 209 916 + 1;
  • 16 954 209 916 ÷ 2 = 8 477 104 958 + 0;
  • 8 477 104 958 ÷ 2 = 4 238 552 479 + 0;
  • 4 238 552 479 ÷ 2 = 2 119 276 239 + 1;
  • 2 119 276 239 ÷ 2 = 1 059 638 119 + 1;
  • 1 059 638 119 ÷ 2 = 529 819 059 + 1;
  • 529 819 059 ÷ 2 = 264 909 529 + 1;
  • 264 909 529 ÷ 2 = 132 454 764 + 1;
  • 132 454 764 ÷ 2 = 66 227 382 + 0;
  • 66 227 382 ÷ 2 = 33 113 691 + 0;
  • 33 113 691 ÷ 2 = 16 556 845 + 1;
  • 16 556 845 ÷ 2 = 8 278 422 + 1;
  • 8 278 422 ÷ 2 = 4 139 211 + 0;
  • 4 139 211 ÷ 2 = 2 069 605 + 1;
  • 2 069 605 ÷ 2 = 1 034 802 + 1;
  • 1 034 802 ÷ 2 = 517 401 + 0;
  • 517 401 ÷ 2 = 258 700 + 1;
  • 258 700 ÷ 2 = 129 350 + 0;
  • 129 350 ÷ 2 = 64 675 + 0;
  • 64 675 ÷ 2 = 32 337 + 1;
  • 32 337 ÷ 2 = 16 168 + 1;
  • 16 168 ÷ 2 = 8 084 + 0;
  • 8 084 ÷ 2 = 4 042 + 0;
  • 4 042 ÷ 2 = 2 021 + 0;
  • 2 021 ÷ 2 = 1 010 + 1;
  • 1 010 ÷ 2 = 505 + 0;
  • 505 ÷ 2 = 252 + 1;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 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.

1 111 111 101 111 083(10) = 11 1111 0010 1000 1100 1011 0110 0111 1100 1101 1011 0010 1011(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 1 111 111 101 111 083(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 111 111 101 111 083(10) = 0000 0000 0000 0011 1111 0010 1000 1100 1011 0110 0111 1100 1101 1011 0010 1011

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

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