Convert 1 001 100 001 100 365 to a Signed Binary (Base 2)

How to convert 1 001 100 001 100 365(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 1 001 100 001 100 365 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;
  • 1 001 100 001 100 365 ÷ 2 = 500 550 000 550 182 + 1;
  • 500 550 000 550 182 ÷ 2 = 250 275 000 275 091 + 0;
  • 250 275 000 275 091 ÷ 2 = 125 137 500 137 545 + 1;
  • 125 137 500 137 545 ÷ 2 = 62 568 750 068 772 + 1;
  • 62 568 750 068 772 ÷ 2 = 31 284 375 034 386 + 0;
  • 31 284 375 034 386 ÷ 2 = 15 642 187 517 193 + 0;
  • 15 642 187 517 193 ÷ 2 = 7 821 093 758 596 + 1;
  • 7 821 093 758 596 ÷ 2 = 3 910 546 879 298 + 0;
  • 3 910 546 879 298 ÷ 2 = 1 955 273 439 649 + 0;
  • 1 955 273 439 649 ÷ 2 = 977 636 719 824 + 1;
  • 977 636 719 824 ÷ 2 = 488 818 359 912 + 0;
  • 488 818 359 912 ÷ 2 = 244 409 179 956 + 0;
  • 244 409 179 956 ÷ 2 = 122 204 589 978 + 0;
  • 122 204 589 978 ÷ 2 = 61 102 294 989 + 0;
  • 61 102 294 989 ÷ 2 = 30 551 147 494 + 1;
  • 30 551 147 494 ÷ 2 = 15 275 573 747 + 0;
  • 15 275 573 747 ÷ 2 = 7 637 786 873 + 1;
  • 7 637 786 873 ÷ 2 = 3 818 893 436 + 1;
  • 3 818 893 436 ÷ 2 = 1 909 446 718 + 0;
  • 1 909 446 718 ÷ 2 = 954 723 359 + 0;
  • 954 723 359 ÷ 2 = 477 361 679 + 1;
  • 477 361 679 ÷ 2 = 238 680 839 + 1;
  • 238 680 839 ÷ 2 = 119 340 419 + 1;
  • 119 340 419 ÷ 2 = 59 670 209 + 1;
  • 59 670 209 ÷ 2 = 29 835 104 + 1;
  • 29 835 104 ÷ 2 = 14 917 552 + 0;
  • 14 917 552 ÷ 2 = 7 458 776 + 0;
  • 7 458 776 ÷ 2 = 3 729 388 + 0;
  • 3 729 388 ÷ 2 = 1 864 694 + 0;
  • 1 864 694 ÷ 2 = 932 347 + 0;
  • 932 347 ÷ 2 = 466 173 + 1;
  • 466 173 ÷ 2 = 233 086 + 1;
  • 233 086 ÷ 2 = 116 543 + 0;
  • 116 543 ÷ 2 = 58 271 + 1;
  • 58 271 ÷ 2 = 29 135 + 1;
  • 29 135 ÷ 2 = 14 567 + 1;
  • 14 567 ÷ 2 = 7 283 + 1;
  • 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.

1 001 100 001 100 365(10) = 11 1000 1110 0111 1110 1100 0001 1111 0011 0100 0010 0100 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:


1 001 100 001 100 365(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 001 100 001 100 365(10) = 0000 0000 0000 0011 1000 1110 0111 1110 1100 0001 1111 0011 0100 0010 0100 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