Convert 1 001 001 110 100 064 to a Signed Binary (Base 2)

How to convert 1 001 001 110 100 064(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 1 001 001 110 100 064 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;
  • 1 001 001 110 100 064 ÷ 2 = 500 500 555 050 032 + 0;
  • 500 500 555 050 032 ÷ 2 = 250 250 277 525 016 + 0;
  • 250 250 277 525 016 ÷ 2 = 125 125 138 762 508 + 0;
  • 125 125 138 762 508 ÷ 2 = 62 562 569 381 254 + 0;
  • 62 562 569 381 254 ÷ 2 = 31 281 284 690 627 + 0;
  • 31 281 284 690 627 ÷ 2 = 15 640 642 345 313 + 1;
  • 15 640 642 345 313 ÷ 2 = 7 820 321 172 656 + 1;
  • 7 820 321 172 656 ÷ 2 = 3 910 160 586 328 + 0;
  • 3 910 160 586 328 ÷ 2 = 1 955 080 293 164 + 0;
  • 1 955 080 293 164 ÷ 2 = 977 540 146 582 + 0;
  • 977 540 146 582 ÷ 2 = 488 770 073 291 + 0;
  • 488 770 073 291 ÷ 2 = 244 385 036 645 + 1;
  • 244 385 036 645 ÷ 2 = 122 192 518 322 + 1;
  • 122 192 518 322 ÷ 2 = 61 096 259 161 + 0;
  • 61 096 259 161 ÷ 2 = 30 548 129 580 + 1;
  • 30 548 129 580 ÷ 2 = 15 274 064 790 + 0;
  • 15 274 064 790 ÷ 2 = 7 637 032 395 + 0;
  • 7 637 032 395 ÷ 2 = 3 818 516 197 + 1;
  • 3 818 516 197 ÷ 2 = 1 909 258 098 + 1;
  • 1 909 258 098 ÷ 2 = 954 629 049 + 0;
  • 954 629 049 ÷ 2 = 477 314 524 + 1;
  • 477 314 524 ÷ 2 = 238 657 262 + 0;
  • 238 657 262 ÷ 2 = 119 328 631 + 0;
  • 119 328 631 ÷ 2 = 59 664 315 + 1;
  • 59 664 315 ÷ 2 = 29 832 157 + 1;
  • 29 832 157 ÷ 2 = 14 916 078 + 1;
  • 14 916 078 ÷ 2 = 7 458 039 + 0;
  • 7 458 039 ÷ 2 = 3 729 019 + 1;
  • 3 729 019 ÷ 2 = 1 864 509 + 1;
  • 1 864 509 ÷ 2 = 932 254 + 1;
  • 932 254 ÷ 2 = 466 127 + 0;
  • 466 127 ÷ 2 = 233 063 + 1;
  • 233 063 ÷ 2 = 116 531 + 1;
  • 116 531 ÷ 2 = 58 265 + 1;
  • 58 265 ÷ 2 = 29 132 + 1;
  • 29 132 ÷ 2 = 14 566 + 0;
  • 14 566 ÷ 2 = 7 283 + 0;
  • 7 283 ÷ 2 = 3 641 + 1;
  • 3 641 ÷ 2 = 1 820 + 1;
  • 1 820 ÷ 2 = 910 + 0;
  • 910 ÷ 2 = 455 + 0;
  • 455 ÷ 2 = 227 + 1;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 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.

1 001 001 110 100 064(10) = 11 1000 1110 0110 0111 1011 1011 1001 0110 0101 1000 0110 0000(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:


1 001 001 110 100 064(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 001 001 110 100 064(10) = 0000 0000 0000 0011 1000 1110 0110 0111 1011 1011 1001 0110 0101 1000 0110 0000

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