Signed: Integer ↗ Binary: 9 123 000 000 000 000 017 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 9 123 000 000 000 000 017(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;
  • 9 123 000 000 000 000 017 ÷ 2 = 4 561 500 000 000 000 008 + 1;
  • 4 561 500 000 000 000 008 ÷ 2 = 2 280 750 000 000 000 004 + 0;
  • 2 280 750 000 000 000 004 ÷ 2 = 1 140 375 000 000 000 002 + 0;
  • 1 140 375 000 000 000 002 ÷ 2 = 570 187 500 000 000 001 + 0;
  • 570 187 500 000 000 001 ÷ 2 = 285 093 750 000 000 000 + 1;
  • 285 093 750 000 000 000 ÷ 2 = 142 546 875 000 000 000 + 0;
  • 142 546 875 000 000 000 ÷ 2 = 71 273 437 500 000 000 + 0;
  • 71 273 437 500 000 000 ÷ 2 = 35 636 718 750 000 000 + 0;
  • 35 636 718 750 000 000 ÷ 2 = 17 818 359 375 000 000 + 0;
  • 17 818 359 375 000 000 ÷ 2 = 8 909 179 687 500 000 + 0;
  • 8 909 179 687 500 000 ÷ 2 = 4 454 589 843 750 000 + 0;
  • 4 454 589 843 750 000 ÷ 2 = 2 227 294 921 875 000 + 0;
  • 2 227 294 921 875 000 ÷ 2 = 1 113 647 460 937 500 + 0;
  • 1 113 647 460 937 500 ÷ 2 = 556 823 730 468 750 + 0;
  • 556 823 730 468 750 ÷ 2 = 278 411 865 234 375 + 0;
  • 278 411 865 234 375 ÷ 2 = 139 205 932 617 187 + 1;
  • 139 205 932 617 187 ÷ 2 = 69 602 966 308 593 + 1;
  • 69 602 966 308 593 ÷ 2 = 34 801 483 154 296 + 1;
  • 34 801 483 154 296 ÷ 2 = 17 400 741 577 148 + 0;
  • 17 400 741 577 148 ÷ 2 = 8 700 370 788 574 + 0;
  • 8 700 370 788 574 ÷ 2 = 4 350 185 394 287 + 0;
  • 4 350 185 394 287 ÷ 2 = 2 175 092 697 143 + 1;
  • 2 175 092 697 143 ÷ 2 = 1 087 546 348 571 + 1;
  • 1 087 546 348 571 ÷ 2 = 543 773 174 285 + 1;
  • 543 773 174 285 ÷ 2 = 271 886 587 142 + 1;
  • 271 886 587 142 ÷ 2 = 135 943 293 571 + 0;
  • 135 943 293 571 ÷ 2 = 67 971 646 785 + 1;
  • 67 971 646 785 ÷ 2 = 33 985 823 392 + 1;
  • 33 985 823 392 ÷ 2 = 16 992 911 696 + 0;
  • 16 992 911 696 ÷ 2 = 8 496 455 848 + 0;
  • 8 496 455 848 ÷ 2 = 4 248 227 924 + 0;
  • 4 248 227 924 ÷ 2 = 2 124 113 962 + 0;
  • 2 124 113 962 ÷ 2 = 1 062 056 981 + 0;
  • 1 062 056 981 ÷ 2 = 531 028 490 + 1;
  • 531 028 490 ÷ 2 = 265 514 245 + 0;
  • 265 514 245 ÷ 2 = 132 757 122 + 1;
  • 132 757 122 ÷ 2 = 66 378 561 + 0;
  • 66 378 561 ÷ 2 = 33 189 280 + 1;
  • 33 189 280 ÷ 2 = 16 594 640 + 0;
  • 16 594 640 ÷ 2 = 8 297 320 + 0;
  • 8 297 320 ÷ 2 = 4 148 660 + 0;
  • 4 148 660 ÷ 2 = 2 074 330 + 0;
  • 2 074 330 ÷ 2 = 1 037 165 + 0;
  • 1 037 165 ÷ 2 = 518 582 + 1;
  • 518 582 ÷ 2 = 259 291 + 0;
  • 259 291 ÷ 2 = 129 645 + 1;
  • 129 645 ÷ 2 = 64 822 + 1;
  • 64 822 ÷ 2 = 32 411 + 0;
  • 32 411 ÷ 2 = 16 205 + 1;
  • 16 205 ÷ 2 = 8 102 + 1;
  • 8 102 ÷ 2 = 4 051 + 0;
  • 4 051 ÷ 2 = 2 025 + 1;
  • 2 025 ÷ 2 = 1 012 + 1;
  • 1 012 ÷ 2 = 506 + 0;
  • 506 ÷ 2 = 253 + 0;
  • 253 ÷ 2 = 126 + 1;
  • 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.


9 123 000 000 000 000 017(10) = 111 1110 1001 1011 0110 1000 0010 1010 0000 1101 1110 0011 1000 0000 0001 0001(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 63.


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, 63,

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 9 123 000 000 000 000 017(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

9 123 000 000 000 000 017(10) = 0111 1110 1001 1011 0110 1000 0010 1010 0000 1101 1110 0011 1000 0000 0001 0001

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

The latest signed integer numbers (that are written in decimal system, in base ten) converted and written as signed binary numbers

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