Convert 1 010 101 000 010 962 to a Signed Binary (Base 2)

How to convert 1 010 101 000 010 962(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 1 010 101 000 010 962 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;
  • 1 010 101 000 010 962 ÷ 2 = 505 050 500 005 481 + 0;
  • 505 050 500 005 481 ÷ 2 = 252 525 250 002 740 + 1;
  • 252 525 250 002 740 ÷ 2 = 126 262 625 001 370 + 0;
  • 126 262 625 001 370 ÷ 2 = 63 131 312 500 685 + 0;
  • 63 131 312 500 685 ÷ 2 = 31 565 656 250 342 + 1;
  • 31 565 656 250 342 ÷ 2 = 15 782 828 125 171 + 0;
  • 15 782 828 125 171 ÷ 2 = 7 891 414 062 585 + 1;
  • 7 891 414 062 585 ÷ 2 = 3 945 707 031 292 + 1;
  • 3 945 707 031 292 ÷ 2 = 1 972 853 515 646 + 0;
  • 1 972 853 515 646 ÷ 2 = 986 426 757 823 + 0;
  • 986 426 757 823 ÷ 2 = 493 213 378 911 + 1;
  • 493 213 378 911 ÷ 2 = 246 606 689 455 + 1;
  • 246 606 689 455 ÷ 2 = 123 303 344 727 + 1;
  • 123 303 344 727 ÷ 2 = 61 651 672 363 + 1;
  • 61 651 672 363 ÷ 2 = 30 825 836 181 + 1;
  • 30 825 836 181 ÷ 2 = 15 412 918 090 + 1;
  • 15 412 918 090 ÷ 2 = 7 706 459 045 + 0;
  • 7 706 459 045 ÷ 2 = 3 853 229 522 + 1;
  • 3 853 229 522 ÷ 2 = 1 926 614 761 + 0;
  • 1 926 614 761 ÷ 2 = 963 307 380 + 1;
  • 963 307 380 ÷ 2 = 481 653 690 + 0;
  • 481 653 690 ÷ 2 = 240 826 845 + 0;
  • 240 826 845 ÷ 2 = 120 413 422 + 1;
  • 120 413 422 ÷ 2 = 60 206 711 + 0;
  • 60 206 711 ÷ 2 = 30 103 355 + 1;
  • 30 103 355 ÷ 2 = 15 051 677 + 1;
  • 15 051 677 ÷ 2 = 7 525 838 + 1;
  • 7 525 838 ÷ 2 = 3 762 919 + 0;
  • 3 762 919 ÷ 2 = 1 881 459 + 1;
  • 1 881 459 ÷ 2 = 940 729 + 1;
  • 940 729 ÷ 2 = 470 364 + 1;
  • 470 364 ÷ 2 = 235 182 + 0;
  • 235 182 ÷ 2 = 117 591 + 0;
  • 117 591 ÷ 2 = 58 795 + 1;
  • 58 795 ÷ 2 = 29 397 + 1;
  • 29 397 ÷ 2 = 14 698 + 1;
  • 14 698 ÷ 2 = 7 349 + 0;
  • 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.

1 010 101 000 010 962(10) = 11 1001 0110 1010 1110 0111 0111 0100 1010 1111 1100 1101 0010(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:


1 010 101 000 010 962(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 010 101 000 010 962(10) = 0000 0000 0000 0011 1001 0110 1010 1110 0111 0111 0100 1010 1111 1100 1101 0010

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