Convert 1 010 110 110 009 325 to a Signed Binary (Base 2)

How to convert 1 010 110 110 009 325(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 1 010 110 110 009 325 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;
  • 1 010 110 110 009 325 ÷ 2 = 505 055 055 004 662 + 1;
  • 505 055 055 004 662 ÷ 2 = 252 527 527 502 331 + 0;
  • 252 527 527 502 331 ÷ 2 = 126 263 763 751 165 + 1;
  • 126 263 763 751 165 ÷ 2 = 63 131 881 875 582 + 1;
  • 63 131 881 875 582 ÷ 2 = 31 565 940 937 791 + 0;
  • 31 565 940 937 791 ÷ 2 = 15 782 970 468 895 + 1;
  • 15 782 970 468 895 ÷ 2 = 7 891 485 234 447 + 1;
  • 7 891 485 234 447 ÷ 2 = 3 945 742 617 223 + 1;
  • 3 945 742 617 223 ÷ 2 = 1 972 871 308 611 + 1;
  • 1 972 871 308 611 ÷ 2 = 986 435 654 305 + 1;
  • 986 435 654 305 ÷ 2 = 493 217 827 152 + 1;
  • 493 217 827 152 ÷ 2 = 246 608 913 576 + 0;
  • 246 608 913 576 ÷ 2 = 123 304 456 788 + 0;
  • 123 304 456 788 ÷ 2 = 61 652 228 394 + 0;
  • 61 652 228 394 ÷ 2 = 30 826 114 197 + 0;
  • 30 826 114 197 ÷ 2 = 15 413 057 098 + 1;
  • 15 413 057 098 ÷ 2 = 7 706 528 549 + 0;
  • 7 706 528 549 ÷ 2 = 3 853 264 274 + 1;
  • 3 853 264 274 ÷ 2 = 1 926 632 137 + 0;
  • 1 926 632 137 ÷ 2 = 963 316 068 + 1;
  • 963 316 068 ÷ 2 = 481 658 034 + 0;
  • 481 658 034 ÷ 2 = 240 829 017 + 0;
  • 240 829 017 ÷ 2 = 120 414 508 + 1;
  • 120 414 508 ÷ 2 = 60 207 254 + 0;
  • 60 207 254 ÷ 2 = 30 103 627 + 0;
  • 30 103 627 ÷ 2 = 15 051 813 + 1;
  • 15 051 813 ÷ 2 = 7 525 906 + 1;
  • 7 525 906 ÷ 2 = 3 762 953 + 0;
  • 3 762 953 ÷ 2 = 1 881 476 + 1;
  • 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.

1 010 110 110 009 325(10) = 11 1001 0110 1011 0000 1001 0110 0100 1010 1000 0111 1110 1101(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:


1 010 110 110 009 325(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 010 110 110 009 325(10) = 0000 0000 0000 0011 1001 0110 1011 0000 1001 0110 0100 1010 1000 0111 1110 1101

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