Signed: Integer ↗ Binary: 1 000 010 000 011 001 185 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 1 000 010 000 011 001 185(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;
  • 1 000 010 000 011 001 185 ÷ 2 = 500 005 000 005 500 592 + 1;
  • 500 005 000 005 500 592 ÷ 2 = 250 002 500 002 750 296 + 0;
  • 250 002 500 002 750 296 ÷ 2 = 125 001 250 001 375 148 + 0;
  • 125 001 250 001 375 148 ÷ 2 = 62 500 625 000 687 574 + 0;
  • 62 500 625 000 687 574 ÷ 2 = 31 250 312 500 343 787 + 0;
  • 31 250 312 500 343 787 ÷ 2 = 15 625 156 250 171 893 + 1;
  • 15 625 156 250 171 893 ÷ 2 = 7 812 578 125 085 946 + 1;
  • 7 812 578 125 085 946 ÷ 2 = 3 906 289 062 542 973 + 0;
  • 3 906 289 062 542 973 ÷ 2 = 1 953 144 531 271 486 + 1;
  • 1 953 144 531 271 486 ÷ 2 = 976 572 265 635 743 + 0;
  • 976 572 265 635 743 ÷ 2 = 488 286 132 817 871 + 1;
  • 488 286 132 817 871 ÷ 2 = 244 143 066 408 935 + 1;
  • 244 143 066 408 935 ÷ 2 = 122 071 533 204 467 + 1;
  • 122 071 533 204 467 ÷ 2 = 61 035 766 602 233 + 1;
  • 61 035 766 602 233 ÷ 2 = 30 517 883 301 116 + 1;
  • 30 517 883 301 116 ÷ 2 = 15 258 941 650 558 + 0;
  • 15 258 941 650 558 ÷ 2 = 7 629 470 825 279 + 0;
  • 7 629 470 825 279 ÷ 2 = 3 814 735 412 639 + 1;
  • 3 814 735 412 639 ÷ 2 = 1 907 367 706 319 + 1;
  • 1 907 367 706 319 ÷ 2 = 953 683 853 159 + 1;
  • 953 683 853 159 ÷ 2 = 476 841 926 579 + 1;
  • 476 841 926 579 ÷ 2 = 238 420 963 289 + 1;
  • 238 420 963 289 ÷ 2 = 119 210 481 644 + 1;
  • 119 210 481 644 ÷ 2 = 59 605 240 822 + 0;
  • 59 605 240 822 ÷ 2 = 29 802 620 411 + 0;
  • 29 802 620 411 ÷ 2 = 14 901 310 205 + 1;
  • 14 901 310 205 ÷ 2 = 7 450 655 102 + 1;
  • 7 450 655 102 ÷ 2 = 3 725 327 551 + 0;
  • 3 725 327 551 ÷ 2 = 1 862 663 775 + 1;
  • 1 862 663 775 ÷ 2 = 931 331 887 + 1;
  • 931 331 887 ÷ 2 = 465 665 943 + 1;
  • 465 665 943 ÷ 2 = 232 832 971 + 1;
  • 232 832 971 ÷ 2 = 116 416 485 + 1;
  • 116 416 485 ÷ 2 = 58 208 242 + 1;
  • 58 208 242 ÷ 2 = 29 104 121 + 0;
  • 29 104 121 ÷ 2 = 14 552 060 + 1;
  • 14 552 060 ÷ 2 = 7 276 030 + 0;
  • 7 276 030 ÷ 2 = 3 638 015 + 0;
  • 3 638 015 ÷ 2 = 1 819 007 + 1;
  • 1 819 007 ÷ 2 = 909 503 + 1;
  • 909 503 ÷ 2 = 454 751 + 1;
  • 454 751 ÷ 2 = 227 375 + 1;
  • 227 375 ÷ 2 = 113 687 + 1;
  • 113 687 ÷ 2 = 56 843 + 1;
  • 56 843 ÷ 2 = 28 421 + 1;
  • 28 421 ÷ 2 = 14 210 + 1;
  • 14 210 ÷ 2 = 7 105 + 0;
  • 7 105 ÷ 2 = 3 552 + 1;
  • 3 552 ÷ 2 = 1 776 + 0;
  • 1 776 ÷ 2 = 888 + 0;
  • 888 ÷ 2 = 444 + 0;
  • 444 ÷ 2 = 222 + 0;
  • 222 ÷ 2 = 111 + 0;
  • 111 ÷ 2 = 55 + 1;
  • 55 ÷ 2 = 27 + 1;
  • 27 ÷ 2 = 13 + 1;
  • 13 ÷ 2 = 6 + 1;
  • 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.


1 000 010 000 011 001 185(10) = 1101 1110 0000 1011 1111 1100 1011 1111 0110 0111 1110 0111 1101 0110 0001(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 60.

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, 60,

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 1 000 010 000 011 001 185(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 000 010 000 011 001 185(10) = 0000 1101 1110 0000 1011 1111 1100 1011 1111 0110 0111 1110 0111 1101 0110 0001

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

More operations on signed integer numbers:

» Signed integer number 1 000 010 000 011 001 184 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 1 000 010 000 011 001 186 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