Signed: Integer ↗ Binary: -2 033 506 857 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 -2 033 506 857(10)
converted and written as a signed binary (base 2) = ?

1. Start with the positive version of the number:

|-2 033 506 857| = 2 033 506 857

2. 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;
  • 2 033 506 857 ÷ 2 = 1 016 753 428 + 1;
  • 1 016 753 428 ÷ 2 = 508 376 714 + 0;
  • 508 376 714 ÷ 2 = 254 188 357 + 0;
  • 254 188 357 ÷ 2 = 127 094 178 + 1;
  • 127 094 178 ÷ 2 = 63 547 089 + 0;
  • 63 547 089 ÷ 2 = 31 773 544 + 1;
  • 31 773 544 ÷ 2 = 15 886 772 + 0;
  • 15 886 772 ÷ 2 = 7 943 386 + 0;
  • 7 943 386 ÷ 2 = 3 971 693 + 0;
  • 3 971 693 ÷ 2 = 1 985 846 + 1;
  • 1 985 846 ÷ 2 = 992 923 + 0;
  • 992 923 ÷ 2 = 496 461 + 1;
  • 496 461 ÷ 2 = 248 230 + 1;
  • 248 230 ÷ 2 = 124 115 + 0;
  • 124 115 ÷ 2 = 62 057 + 1;
  • 62 057 ÷ 2 = 31 028 + 1;
  • 31 028 ÷ 2 = 15 514 + 0;
  • 15 514 ÷ 2 = 7 757 + 0;
  • 7 757 ÷ 2 = 3 878 + 1;
  • 3 878 ÷ 2 = 1 939 + 0;
  • 1 939 ÷ 2 = 969 + 1;
  • 969 ÷ 2 = 484 + 1;
  • 484 ÷ 2 = 242 + 0;
  • 242 ÷ 2 = 121 + 0;
  • 121 ÷ 2 = 60 + 1;
  • 60 ÷ 2 = 30 + 0;
  • 30 ÷ 2 = 15 + 0;
  • 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:

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


2 033 506 857(10) = 111 1001 0011 0100 1101 1010 0010 1001(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:


2 033 506 857(10) = 0111 1001 0011 0100 1101 1010 0010 1001


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...


Number -2 033 506 857(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-2 033 506 857(10) = 1111 1001 0011 0100 1101 1010 0010 1001

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

The latest signed integer numbers (that are written in decimal system, in base ten) converted and written as signed binary numbers

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