Two's Complement: Integer ↗ Binary: 11 001 109 972 Convert the Integer Number to a Signed Binary in Two's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 11 001 109 972(10) converted and written as a signed binary in two's complement representation (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;
  • 11 001 109 972 ÷ 2 = 5 500 554 986 + 0;
  • 5 500 554 986 ÷ 2 = 2 750 277 493 + 0;
  • 2 750 277 493 ÷ 2 = 1 375 138 746 + 1;
  • 1 375 138 746 ÷ 2 = 687 569 373 + 0;
  • 687 569 373 ÷ 2 = 343 784 686 + 1;
  • 343 784 686 ÷ 2 = 171 892 343 + 0;
  • 171 892 343 ÷ 2 = 85 946 171 + 1;
  • 85 946 171 ÷ 2 = 42 973 085 + 1;
  • 42 973 085 ÷ 2 = 21 486 542 + 1;
  • 21 486 542 ÷ 2 = 10 743 271 + 0;
  • 10 743 271 ÷ 2 = 5 371 635 + 1;
  • 5 371 635 ÷ 2 = 2 685 817 + 1;
  • 2 685 817 ÷ 2 = 1 342 908 + 1;
  • 1 342 908 ÷ 2 = 671 454 + 0;
  • 671 454 ÷ 2 = 335 727 + 0;
  • 335 727 ÷ 2 = 167 863 + 1;
  • 167 863 ÷ 2 = 83 931 + 1;
  • 83 931 ÷ 2 = 41 965 + 1;
  • 41 965 ÷ 2 = 20 982 + 1;
  • 20 982 ÷ 2 = 10 491 + 0;
  • 10 491 ÷ 2 = 5 245 + 1;
  • 5 245 ÷ 2 = 2 622 + 1;
  • 2 622 ÷ 2 = 1 311 + 0;
  • 1 311 ÷ 2 = 655 + 1;
  • 655 ÷ 2 = 327 + 1;
  • 327 ÷ 2 = 163 + 1;
  • 163 ÷ 2 = 81 + 1;
  • 81 ÷ 2 = 40 + 1;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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.


11 001 109 972(10) = 10 1000 1111 1011 0111 1001 1101 1101 0100(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 34.

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) indicates 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, 34,

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 11 001 109 972(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:

11 001 109 972(10) = 0000 0000 0000 0000 0000 0000 0000 0010 1000 1111 1011 0111 1001 1101 1101 0100

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

More operations on integers written as signed binary numbers in two's complement representation:

» Signed integer number 11 001 109 971 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

» Signed integer number 11 001 109 973 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

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How to convert signed integers from decimal system to signed binary in two's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in two's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number, keeping track of each remainder, until 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 must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will be 0, correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all 0 bits with 1s and all 1 bits with 0s (reversing the digits).
  • 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

  • 1. Start with the positive version of the number: |-60| = 60
  • 2. Divide repeatedly 60 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 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, by taking all the remainders starting from the bottom of the list constructed above:
    60(10) = 11 1100(2)
  • 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
    60(10) = 0011 1100(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
    !(0011 1100) = 1100 0011
  • 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
    -60(10) = 1100 0011 + 1 = 1100 0100
  • Number -60(10), signed integer, converted from decimal system (base 10) to signed binary two's complement representation = 1100 0100