Signed: Integer ↗ Binary: 1 001 110 001 110 017 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 1 001 110 001 110 017(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;
  • 1 001 110 001 110 017 ÷ 2 = 500 555 000 555 008 + 1;
  • 500 555 000 555 008 ÷ 2 = 250 277 500 277 504 + 0;
  • 250 277 500 277 504 ÷ 2 = 125 138 750 138 752 + 0;
  • 125 138 750 138 752 ÷ 2 = 62 569 375 069 376 + 0;
  • 62 569 375 069 376 ÷ 2 = 31 284 687 534 688 + 0;
  • 31 284 687 534 688 ÷ 2 = 15 642 343 767 344 + 0;
  • 15 642 343 767 344 ÷ 2 = 7 821 171 883 672 + 0;
  • 7 821 171 883 672 ÷ 2 = 3 910 585 941 836 + 0;
  • 3 910 585 941 836 ÷ 2 = 1 955 292 970 918 + 0;
  • 1 955 292 970 918 ÷ 2 = 977 646 485 459 + 0;
  • 977 646 485 459 ÷ 2 = 488 823 242 729 + 1;
  • 488 823 242 729 ÷ 2 = 244 411 621 364 + 1;
  • 244 411 621 364 ÷ 2 = 122 205 810 682 + 0;
  • 122 205 810 682 ÷ 2 = 61 102 905 341 + 0;
  • 61 102 905 341 ÷ 2 = 30 551 452 670 + 1;
  • 30 551 452 670 ÷ 2 = 15 275 726 335 + 0;
  • 15 275 726 335 ÷ 2 = 7 637 863 167 + 1;
  • 7 637 863 167 ÷ 2 = 3 818 931 583 + 1;
  • 3 818 931 583 ÷ 2 = 1 909 465 791 + 1;
  • 1 909 465 791 ÷ 2 = 954 732 895 + 1;
  • 954 732 895 ÷ 2 = 477 366 447 + 1;
  • 477 366 447 ÷ 2 = 238 683 223 + 1;
  • 238 683 223 ÷ 2 = 119 341 611 + 1;
  • 119 341 611 ÷ 2 = 59 670 805 + 1;
  • 59 670 805 ÷ 2 = 29 835 402 + 1;
  • 29 835 402 ÷ 2 = 14 917 701 + 0;
  • 14 917 701 ÷ 2 = 7 458 850 + 1;
  • 7 458 850 ÷ 2 = 3 729 425 + 0;
  • 3 729 425 ÷ 2 = 1 864 712 + 1;
  • 1 864 712 ÷ 2 = 932 356 + 0;
  • 932 356 ÷ 2 = 466 178 + 0;
  • 466 178 ÷ 2 = 233 089 + 0;
  • 233 089 ÷ 2 = 116 544 + 1;
  • 116 544 ÷ 2 = 58 272 + 0;
  • 58 272 ÷ 2 = 29 136 + 0;
  • 29 136 ÷ 2 = 14 568 + 0;
  • 14 568 ÷ 2 = 7 284 + 0;
  • 7 284 ÷ 2 = 3 642 + 0;
  • 3 642 ÷ 2 = 1 821 + 0;
  • 1 821 ÷ 2 = 910 + 1;
  • 910 ÷ 2 = 455 + 0;
  • 455 ÷ 2 = 227 + 1;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 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.


1 001 110 001 110 017(10) = 11 1000 1110 1000 0001 0001 0101 1111 1111 0100 1100 0000 0001(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 1 001 110 001 110 017(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 001 110 001 110 017(10) = 0000 0000 0000 0011 1000 1110 1000 0001 0001 0101 1111 1111 0100 1100 0000 0001

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

More operations on signed integer numbers:

» Signed integer number 1 001 110 001 110 016 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 1 001 110 001 110 018 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