Signed: Integer ↗ Binary: 1 101 100 011 109 995 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 1 101 100 011 109 995(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;
  • 1 101 100 011 109 995 ÷ 2 = 550 550 005 554 997 + 1;
  • 550 550 005 554 997 ÷ 2 = 275 275 002 777 498 + 1;
  • 275 275 002 777 498 ÷ 2 = 137 637 501 388 749 + 0;
  • 137 637 501 388 749 ÷ 2 = 68 818 750 694 374 + 1;
  • 68 818 750 694 374 ÷ 2 = 34 409 375 347 187 + 0;
  • 34 409 375 347 187 ÷ 2 = 17 204 687 673 593 + 1;
  • 17 204 687 673 593 ÷ 2 = 8 602 343 836 796 + 1;
  • 8 602 343 836 796 ÷ 2 = 4 301 171 918 398 + 0;
  • 4 301 171 918 398 ÷ 2 = 2 150 585 959 199 + 0;
  • 2 150 585 959 199 ÷ 2 = 1 075 292 979 599 + 1;
  • 1 075 292 979 599 ÷ 2 = 537 646 489 799 + 1;
  • 537 646 489 799 ÷ 2 = 268 823 244 899 + 1;
  • 268 823 244 899 ÷ 2 = 134 411 622 449 + 1;
  • 134 411 622 449 ÷ 2 = 67 205 811 224 + 1;
  • 67 205 811 224 ÷ 2 = 33 602 905 612 + 0;
  • 33 602 905 612 ÷ 2 = 16 801 452 806 + 0;
  • 16 801 452 806 ÷ 2 = 8 400 726 403 + 0;
  • 8 400 726 403 ÷ 2 = 4 200 363 201 + 1;
  • 4 200 363 201 ÷ 2 = 2 100 181 600 + 1;
  • 2 100 181 600 ÷ 2 = 1 050 090 800 + 0;
  • 1 050 090 800 ÷ 2 = 525 045 400 + 0;
  • 525 045 400 ÷ 2 = 262 522 700 + 0;
  • 262 522 700 ÷ 2 = 131 261 350 + 0;
  • 131 261 350 ÷ 2 = 65 630 675 + 0;
  • 65 630 675 ÷ 2 = 32 815 337 + 1;
  • 32 815 337 ÷ 2 = 16 407 668 + 1;
  • 16 407 668 ÷ 2 = 8 203 834 + 0;
  • 8 203 834 ÷ 2 = 4 101 917 + 0;
  • 4 101 917 ÷ 2 = 2 050 958 + 1;
  • 2 050 958 ÷ 2 = 1 025 479 + 0;
  • 1 025 479 ÷ 2 = 512 739 + 1;
  • 512 739 ÷ 2 = 256 369 + 1;
  • 256 369 ÷ 2 = 128 184 + 1;
  • 128 184 ÷ 2 = 64 092 + 0;
  • 64 092 ÷ 2 = 32 046 + 0;
  • 32 046 ÷ 2 = 16 023 + 0;
  • 16 023 ÷ 2 = 8 011 + 1;
  • 8 011 ÷ 2 = 4 005 + 1;
  • 4 005 ÷ 2 = 2 002 + 1;
  • 2 002 ÷ 2 = 1 001 + 0;
  • 1 001 ÷ 2 = 500 + 1;
  • 500 ÷ 2 = 250 + 0;
  • 250 ÷ 2 = 125 + 0;
  • 125 ÷ 2 = 62 + 1;
  • 62 ÷ 2 = 31 + 0;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.


1 101 100 011 109 995(10) = 11 1110 1001 0111 0001 1101 0011 0000 0110 0011 1110 0110 1011(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:


Number 1 101 100 011 109 995(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 101 100 011 109 995(10) = 0000 0000 0000 0011 1110 1001 0111 0001 1101 0011 0000 0110 0011 1110 0110 1011

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

More operations on signed integer numbers:

» Signed integer number 1 101 100 011 109 994 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 1 101 100 011 109 996 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