Signed: Integer ↗ Binary: 50 000 000 000 096 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number 50 000 000 000 096(10)
converted and written as a signed binary (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 50 000 000 000 096 ÷ 2 = 25 000 000 000 048 + 0;
  • 25 000 000 000 048 ÷ 2 = 12 500 000 000 024 + 0;
  • 12 500 000 000 024 ÷ 2 = 6 250 000 000 012 + 0;
  • 6 250 000 000 012 ÷ 2 = 3 125 000 000 006 + 0;
  • 3 125 000 000 006 ÷ 2 = 1 562 500 000 003 + 0;
  • 1 562 500 000 003 ÷ 2 = 781 250 000 001 + 1;
  • 781 250 000 001 ÷ 2 = 390 625 000 000 + 1;
  • 390 625 000 000 ÷ 2 = 195 312 500 000 + 0;
  • 195 312 500 000 ÷ 2 = 97 656 250 000 + 0;
  • 97 656 250 000 ÷ 2 = 48 828 125 000 + 0;
  • 48 828 125 000 ÷ 2 = 24 414 062 500 + 0;
  • 24 414 062 500 ÷ 2 = 12 207 031 250 + 0;
  • 12 207 031 250 ÷ 2 = 6 103 515 625 + 0;
  • 6 103 515 625 ÷ 2 = 3 051 757 812 + 1;
  • 3 051 757 812 ÷ 2 = 1 525 878 906 + 0;
  • 1 525 878 906 ÷ 2 = 762 939 453 + 0;
  • 762 939 453 ÷ 2 = 381 469 726 + 1;
  • 381 469 726 ÷ 2 = 190 734 863 + 0;
  • 190 734 863 ÷ 2 = 95 367 431 + 1;
  • 95 367 431 ÷ 2 = 47 683 715 + 1;
  • 47 683 715 ÷ 2 = 23 841 857 + 1;
  • 23 841 857 ÷ 2 = 11 920 928 + 1;
  • 11 920 928 ÷ 2 = 5 960 464 + 0;
  • 5 960 464 ÷ 2 = 2 980 232 + 0;
  • 2 980 232 ÷ 2 = 1 490 116 + 0;
  • 1 490 116 ÷ 2 = 745 058 + 0;
  • 745 058 ÷ 2 = 372 529 + 0;
  • 372 529 ÷ 2 = 186 264 + 1;
  • 186 264 ÷ 2 = 93 132 + 0;
  • 93 132 ÷ 2 = 46 566 + 0;
  • 46 566 ÷ 2 = 23 283 + 0;
  • 23 283 ÷ 2 = 11 641 + 1;
  • 11 641 ÷ 2 = 5 820 + 1;
  • 5 820 ÷ 2 = 2 910 + 0;
  • 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.


50 000 000 000 096(10) = 10 1101 0111 1001 1000 1000 0011 1101 0010 0000 0110 0000(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 46.

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, 46,

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:


Number 50 000 000 000 096(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

50 000 000 000 096(10) = 0000 0000 0000 0000 0010 1101 0111 1001 1000 1000 0011 1101 0010 0000 0110 0000

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

More operations on signed integer numbers:

» Signed integer number 50 000 000 000 095 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 50 000 000 000 097 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

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How to convert signed integers from decimal system 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