Integer to Signed Binary: Number 110 010 110 010 035 Converted and Written as a Signed Binary. Base Ten Decimal System Conversion

Integer number 110 010 110 010 035(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;
  • 110 010 110 010 035 ÷ 2 = 55 005 055 005 017 + 1;
  • 55 005 055 005 017 ÷ 2 = 27 502 527 502 508 + 1;
  • 27 502 527 502 508 ÷ 2 = 13 751 263 751 254 + 0;
  • 13 751 263 751 254 ÷ 2 = 6 875 631 875 627 + 0;
  • 6 875 631 875 627 ÷ 2 = 3 437 815 937 813 + 1;
  • 3 437 815 937 813 ÷ 2 = 1 718 907 968 906 + 1;
  • 1 718 907 968 906 ÷ 2 = 859 453 984 453 + 0;
  • 859 453 984 453 ÷ 2 = 429 726 992 226 + 1;
  • 429 726 992 226 ÷ 2 = 214 863 496 113 + 0;
  • 214 863 496 113 ÷ 2 = 107 431 748 056 + 1;
  • 107 431 748 056 ÷ 2 = 53 715 874 028 + 0;
  • 53 715 874 028 ÷ 2 = 26 857 937 014 + 0;
  • 26 857 937 014 ÷ 2 = 13 428 968 507 + 0;
  • 13 428 968 507 ÷ 2 = 6 714 484 253 + 1;
  • 6 714 484 253 ÷ 2 = 3 357 242 126 + 1;
  • 3 357 242 126 ÷ 2 = 1 678 621 063 + 0;
  • 1 678 621 063 ÷ 2 = 839 310 531 + 1;
  • 839 310 531 ÷ 2 = 419 655 265 + 1;
  • 419 655 265 ÷ 2 = 209 827 632 + 1;
  • 209 827 632 ÷ 2 = 104 913 816 + 0;
  • 104 913 816 ÷ 2 = 52 456 908 + 0;
  • 52 456 908 ÷ 2 = 26 228 454 + 0;
  • 26 228 454 ÷ 2 = 13 114 227 + 0;
  • 13 114 227 ÷ 2 = 6 557 113 + 1;
  • 6 557 113 ÷ 2 = 3 278 556 + 1;
  • 3 278 556 ÷ 2 = 1 639 278 + 0;
  • 1 639 278 ÷ 2 = 819 639 + 0;
  • 819 639 ÷ 2 = 409 819 + 1;
  • 409 819 ÷ 2 = 204 909 + 1;
  • 204 909 ÷ 2 = 102 454 + 1;
  • 102 454 ÷ 2 = 51 227 + 0;
  • 51 227 ÷ 2 = 25 613 + 1;
  • 25 613 ÷ 2 = 12 806 + 1;
  • 12 806 ÷ 2 = 6 403 + 0;
  • 6 403 ÷ 2 = 3 201 + 1;
  • 3 201 ÷ 2 = 1 600 + 1;
  • 1 600 ÷ 2 = 800 + 0;
  • 800 ÷ 2 = 400 + 0;
  • 400 ÷ 2 = 200 + 0;
  • 200 ÷ 2 = 100 + 0;
  • 100 ÷ 2 = 50 + 0;
  • 50 ÷ 2 = 25 + 0;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 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.

110 010 110 010 035(10) = 110 0100 0000 1101 1011 1001 1000 0111 0110 0010 1011 0011(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 110 010 110 010 035(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

110 010 110 010 035(10) = 0000 0000 0000 0000 0110 0100 0000 1101 1011 1001 1000 0111 0110 0010 1011 0011

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

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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