Convert 1 010 110 001 011 326 to a Signed Binary (Base 2)

How to convert 1 010 110 001 011 326(10), a signed base 10 integer number? How to write it as a signed binary code in base 2

What are the required steps to convert base 10 integer
number 1 010 110 001 011 326 to signed binary code (in base 2)?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 010 110 001 011 326 ÷ 2 = 505 055 000 505 663 + 0;
  • 505 055 000 505 663 ÷ 2 = 252 527 500 252 831 + 1;
  • 252 527 500 252 831 ÷ 2 = 126 263 750 126 415 + 1;
  • 126 263 750 126 415 ÷ 2 = 63 131 875 063 207 + 1;
  • 63 131 875 063 207 ÷ 2 = 31 565 937 531 603 + 1;
  • 31 565 937 531 603 ÷ 2 = 15 782 968 765 801 + 1;
  • 15 782 968 765 801 ÷ 2 = 7 891 484 382 900 + 1;
  • 7 891 484 382 900 ÷ 2 = 3 945 742 191 450 + 0;
  • 3 945 742 191 450 ÷ 2 = 1 972 871 095 725 + 0;
  • 1 972 871 095 725 ÷ 2 = 986 435 547 862 + 1;
  • 986 435 547 862 ÷ 2 = 493 217 773 931 + 0;
  • 493 217 773 931 ÷ 2 = 246 608 886 965 + 1;
  • 246 608 886 965 ÷ 2 = 123 304 443 482 + 1;
  • 123 304 443 482 ÷ 2 = 61 652 221 741 + 0;
  • 61 652 221 741 ÷ 2 = 30 826 110 870 + 1;
  • 30 826 110 870 ÷ 2 = 15 413 055 435 + 0;
  • 15 413 055 435 ÷ 2 = 7 706 527 717 + 1;
  • 7 706 527 717 ÷ 2 = 3 853 263 858 + 1;
  • 3 853 263 858 ÷ 2 = 1 926 631 929 + 0;
  • 1 926 631 929 ÷ 2 = 963 315 964 + 1;
  • 963 315 964 ÷ 2 = 481 657 982 + 0;
  • 481 657 982 ÷ 2 = 240 828 991 + 0;
  • 240 828 991 ÷ 2 = 120 414 495 + 1;
  • 120 414 495 ÷ 2 = 60 207 247 + 1;
  • 60 207 247 ÷ 2 = 30 103 623 + 1;
  • 30 103 623 ÷ 2 = 15 051 811 + 1;
  • 15 051 811 ÷ 2 = 7 525 905 + 1;
  • 7 525 905 ÷ 2 = 3 762 952 + 1;
  • 3 762 952 ÷ 2 = 1 881 476 + 0;
  • 1 881 476 ÷ 2 = 940 738 + 0;
  • 940 738 ÷ 2 = 470 369 + 0;
  • 470 369 ÷ 2 = 235 184 + 1;
  • 235 184 ÷ 2 = 117 592 + 0;
  • 117 592 ÷ 2 = 58 796 + 0;
  • 58 796 ÷ 2 = 29 398 + 0;
  • 29 398 ÷ 2 = 14 699 + 0;
  • 14 699 ÷ 2 = 7 349 + 1;
  • 7 349 ÷ 2 = 3 674 + 1;
  • 3 674 ÷ 2 = 1 837 + 0;
  • 1 837 ÷ 2 = 918 + 1;
  • 918 ÷ 2 = 459 + 0;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 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.

1 010 110 001 011 326(10) = 11 1001 0110 1011 0000 1000 1111 1100 1011 0101 1010 0111 1110(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:


1 010 110 001 011 326(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 010 110 001 011 326(10) = 0000 0000 0000 0011 1001 0110 1011 0000 1000 1111 1100 1011 0101 1010 0111 1110

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

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How to convert signed base 10 integers in decimal 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