Convert -1 283 333 373 to a Signed Binary (Base 2)

How to convert -1 283 333 373(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 -1 283 333 373 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. Start with the positive version of the number:

|-1 283 333 373| = 1 283 333 373

2. 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;
  • 1 283 333 373 ÷ 2 = 641 666 686 + 1;
  • 641 666 686 ÷ 2 = 320 833 343 + 0;
  • 320 833 343 ÷ 2 = 160 416 671 + 1;
  • 160 416 671 ÷ 2 = 80 208 335 + 1;
  • 80 208 335 ÷ 2 = 40 104 167 + 1;
  • 40 104 167 ÷ 2 = 20 052 083 + 1;
  • 20 052 083 ÷ 2 = 10 026 041 + 1;
  • 10 026 041 ÷ 2 = 5 013 020 + 1;
  • 5 013 020 ÷ 2 = 2 506 510 + 0;
  • 2 506 510 ÷ 2 = 1 253 255 + 0;
  • 1 253 255 ÷ 2 = 626 627 + 1;
  • 626 627 ÷ 2 = 313 313 + 1;
  • 313 313 ÷ 2 = 156 656 + 1;
  • 156 656 ÷ 2 = 78 328 + 0;
  • 78 328 ÷ 2 = 39 164 + 0;
  • 39 164 ÷ 2 = 19 582 + 0;
  • 19 582 ÷ 2 = 9 791 + 0;
  • 9 791 ÷ 2 = 4 895 + 1;
  • 4 895 ÷ 2 = 2 447 + 1;
  • 2 447 ÷ 2 = 1 223 + 1;
  • 1 223 ÷ 2 = 611 + 1;
  • 611 ÷ 2 = 305 + 1;
  • 305 ÷ 2 = 152 + 1;
  • 152 ÷ 2 = 76 + 0;
  • 76 ÷ 2 = 38 + 0;
  • 38 ÷ 2 = 19 + 0;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

1 283 333 373(10) = 100 1100 0111 1110 0001 1100 1111 1101(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 31.

  • 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, 31,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 32.


5. Get the positive binary computer representation on 32 bits (4 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:


1 283 333 373(10) = 0100 1100 0111 1110 0001 1100 1111 1101

6. Get the negative integer number representation:

To get the negative integer number representation on 32 bits (4 Bytes),

... change the first bit (the leftmost), from 0 to 1...


-1 283 333 373(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-1 283 333 373(10) = 1100 1100 0111 1110 0001 1100 1111 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