Signed: Integer ↗ Binary: -1 988 795 358 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 -1 988 795 358(10)
converted and written as a signed binary (base 2) = ?

1. Start with the positive version of the number:

|-1 988 795 358| = 1 988 795 358

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;
  • 1 988 795 358 ÷ 2 = 994 397 679 + 0;
  • 994 397 679 ÷ 2 = 497 198 839 + 1;
  • 497 198 839 ÷ 2 = 248 599 419 + 1;
  • 248 599 419 ÷ 2 = 124 299 709 + 1;
  • 124 299 709 ÷ 2 = 62 149 854 + 1;
  • 62 149 854 ÷ 2 = 31 074 927 + 0;
  • 31 074 927 ÷ 2 = 15 537 463 + 1;
  • 15 537 463 ÷ 2 = 7 768 731 + 1;
  • 7 768 731 ÷ 2 = 3 884 365 + 1;
  • 3 884 365 ÷ 2 = 1 942 182 + 1;
  • 1 942 182 ÷ 2 = 971 091 + 0;
  • 971 091 ÷ 2 = 485 545 + 1;
  • 485 545 ÷ 2 = 242 772 + 1;
  • 242 772 ÷ 2 = 121 386 + 0;
  • 121 386 ÷ 2 = 60 693 + 0;
  • 60 693 ÷ 2 = 30 346 + 1;
  • 30 346 ÷ 2 = 15 173 + 0;
  • 15 173 ÷ 2 = 7 586 + 1;
  • 7 586 ÷ 2 = 3 793 + 0;
  • 3 793 ÷ 2 = 1 896 + 1;
  • 1 896 ÷ 2 = 948 + 0;
  • 948 ÷ 2 = 474 + 0;
  • 474 ÷ 2 = 237 + 0;
  • 237 ÷ 2 = 118 + 1;
  • 118 ÷ 2 = 59 + 0;
  • 59 ÷ 2 = 29 + 1;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 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.


1 988 795 358(10) = 111 0110 1000 1010 1001 1011 1101 1110(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:


1 988 795 358(10) = 0111 0110 1000 1010 1001 1011 1101 1110


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 -1 988 795 358(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-1 988 795 358(10) = 1111 0110 1000 1010 1001 1011 1101 1110

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

More operations on signed integer numbers:

» Signed integer number -1 988 795 359 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number -1 988 795 357 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