Convert 100 010 101 110 790 to a Signed Binary (Base 2)

How to convert 100 010 101 110 790(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 100 010 101 110 790 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;
  • 100 010 101 110 790 ÷ 2 = 50 005 050 555 395 + 0;
  • 50 005 050 555 395 ÷ 2 = 25 002 525 277 697 + 1;
  • 25 002 525 277 697 ÷ 2 = 12 501 262 638 848 + 1;
  • 12 501 262 638 848 ÷ 2 = 6 250 631 319 424 + 0;
  • 6 250 631 319 424 ÷ 2 = 3 125 315 659 712 + 0;
  • 3 125 315 659 712 ÷ 2 = 1 562 657 829 856 + 0;
  • 1 562 657 829 856 ÷ 2 = 781 328 914 928 + 0;
  • 781 328 914 928 ÷ 2 = 390 664 457 464 + 0;
  • 390 664 457 464 ÷ 2 = 195 332 228 732 + 0;
  • 195 332 228 732 ÷ 2 = 97 666 114 366 + 0;
  • 97 666 114 366 ÷ 2 = 48 833 057 183 + 0;
  • 48 833 057 183 ÷ 2 = 24 416 528 591 + 1;
  • 24 416 528 591 ÷ 2 = 12 208 264 295 + 1;
  • 12 208 264 295 ÷ 2 = 6 104 132 147 + 1;
  • 6 104 132 147 ÷ 2 = 3 052 066 073 + 1;
  • 3 052 066 073 ÷ 2 = 1 526 033 036 + 1;
  • 1 526 033 036 ÷ 2 = 763 016 518 + 0;
  • 763 016 518 ÷ 2 = 381 508 259 + 0;
  • 381 508 259 ÷ 2 = 190 754 129 + 1;
  • 190 754 129 ÷ 2 = 95 377 064 + 1;
  • 95 377 064 ÷ 2 = 47 688 532 + 0;
  • 47 688 532 ÷ 2 = 23 844 266 + 0;
  • 23 844 266 ÷ 2 = 11 922 133 + 0;
  • 11 922 133 ÷ 2 = 5 961 066 + 1;
  • 5 961 066 ÷ 2 = 2 980 533 + 0;
  • 2 980 533 ÷ 2 = 1 490 266 + 1;
  • 1 490 266 ÷ 2 = 745 133 + 0;
  • 745 133 ÷ 2 = 372 566 + 1;
  • 372 566 ÷ 2 = 186 283 + 0;
  • 186 283 ÷ 2 = 93 141 + 1;
  • 93 141 ÷ 2 = 46 570 + 1;
  • 46 570 ÷ 2 = 23 285 + 0;
  • 23 285 ÷ 2 = 11 642 + 1;
  • 11 642 ÷ 2 = 5 821 + 0;
  • 5 821 ÷ 2 = 2 910 + 1;
  • 2 910 ÷ 2 = 1 455 + 0;
  • 1 455 ÷ 2 = 727 + 1;
  • 727 ÷ 2 = 363 + 1;
  • 363 ÷ 2 = 181 + 1;
  • 181 ÷ 2 = 90 + 1;
  • 90 ÷ 2 = 45 + 0;
  • 45 ÷ 2 = 22 + 1;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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.

100 010 101 110 790(10) = 101 1010 1111 0101 0110 1010 1000 1100 1111 1000 0000 0110(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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, 47,

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:


100 010 101 110 790(10) Base 10 integer number converted and written as a signed binary code (in base 2):

100 010 101 110 790(10) = 0000 0000 0000 0000 0101 1010 1111 0101 0110 1010 1000 1100 1111 1000 0000 0110

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