Signed: Integer ↗ Binary: 2 001 112 072 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 2 001 112 072(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;
  • 2 001 112 072 ÷ 2 = 1 000 556 036 + 0;
  • 1 000 556 036 ÷ 2 = 500 278 018 + 0;
  • 500 278 018 ÷ 2 = 250 139 009 + 0;
  • 250 139 009 ÷ 2 = 125 069 504 + 1;
  • 125 069 504 ÷ 2 = 62 534 752 + 0;
  • 62 534 752 ÷ 2 = 31 267 376 + 0;
  • 31 267 376 ÷ 2 = 15 633 688 + 0;
  • 15 633 688 ÷ 2 = 7 816 844 + 0;
  • 7 816 844 ÷ 2 = 3 908 422 + 0;
  • 3 908 422 ÷ 2 = 1 954 211 + 0;
  • 1 954 211 ÷ 2 = 977 105 + 1;
  • 977 105 ÷ 2 = 488 552 + 1;
  • 488 552 ÷ 2 = 244 276 + 0;
  • 244 276 ÷ 2 = 122 138 + 0;
  • 122 138 ÷ 2 = 61 069 + 0;
  • 61 069 ÷ 2 = 30 534 + 1;
  • 30 534 ÷ 2 = 15 267 + 0;
  • 15 267 ÷ 2 = 7 633 + 1;
  • 7 633 ÷ 2 = 3 816 + 1;
  • 3 816 ÷ 2 = 1 908 + 0;
  • 1 908 ÷ 2 = 954 + 0;
  • 954 ÷ 2 = 477 + 0;
  • 477 ÷ 2 = 238 + 1;
  • 238 ÷ 2 = 119 + 0;
  • 119 ÷ 2 = 59 + 1;
  • 59 ÷ 2 = 29 + 1;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 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.


2 001 112 072(10) = 111 0111 0100 0110 1000 1100 0000 1000(2)


3. 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.


4. 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:


Number 2 001 112 072(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

2 001 112 072(10) = 0111 0111 0100 0110 1000 1100 0000 1000

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

More operations on signed integer numbers:

» Signed integer number 2 001 112 071 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 2 001 112 073 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

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

Convert the base ten decimal system integer number 3,690, write it as a signed binary written in base two May 02 22:09 UTC (GMT)
Convert the base ten decimal system integer number 1,099,511,627,823, write it as a signed binary written in base two May 02 22:09 UTC (GMT)
Convert the base ten decimal system integer number 1,412,158, write it as a signed binary written in base two May 02 22:09 UTC (GMT)
Convert the base ten decimal system integer number 1,099,511,627,823, write it as a signed binary written in base two May 02 22:09 UTC (GMT)
Convert the base ten decimal system integer number 3,690, write it as a signed binary written in base two May 02 22:09 UTC (GMT)
Convert the base ten decimal system integer number 1,412,158, write it as a signed binary written in base two May 02 22:09 UTC (GMT)
Convert the base ten decimal system integer number 110,010,100,975, write it as a signed binary written in base two May 02 22:08 UTC (GMT)
Convert the base ten decimal system integer number 100,000,000,002, write it as a signed binary written in base two May 02 22:07 UTC (GMT)
Convert the base ten decimal system integer number -5,287, write it as a signed binary written in base two May 02 22:07 UTC (GMT)
Convert the base ten decimal system integer number 1,101,010,110,110,148, write it as a signed binary written in base two May 02 22:07 UTC (GMT)
All the decimal system integer numbers (written 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