Integer as Two's Complement Binary: Number 1 011 101 110 909 Converted and Written as a Signed Binary in Two's Complement Representation

Integer number 1 011 101 110 909(10) written as a signed binary in two's complement representation

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;
  • 1 011 101 110 909 ÷ 2 = 505 550 555 454 + 1;
  • 505 550 555 454 ÷ 2 = 252 775 277 727 + 0;
  • 252 775 277 727 ÷ 2 = 126 387 638 863 + 1;
  • 126 387 638 863 ÷ 2 = 63 193 819 431 + 1;
  • 63 193 819 431 ÷ 2 = 31 596 909 715 + 1;
  • 31 596 909 715 ÷ 2 = 15 798 454 857 + 1;
  • 15 798 454 857 ÷ 2 = 7 899 227 428 + 1;
  • 7 899 227 428 ÷ 2 = 3 949 613 714 + 0;
  • 3 949 613 714 ÷ 2 = 1 974 806 857 + 0;
  • 1 974 806 857 ÷ 2 = 987 403 428 + 1;
  • 987 403 428 ÷ 2 = 493 701 714 + 0;
  • 493 701 714 ÷ 2 = 246 850 857 + 0;
  • 246 850 857 ÷ 2 = 123 425 428 + 1;
  • 123 425 428 ÷ 2 = 61 712 714 + 0;
  • 61 712 714 ÷ 2 = 30 856 357 + 0;
  • 30 856 357 ÷ 2 = 15 428 178 + 1;
  • 15 428 178 ÷ 2 = 7 714 089 + 0;
  • 7 714 089 ÷ 2 = 3 857 044 + 1;
  • 3 857 044 ÷ 2 = 1 928 522 + 0;
  • 1 928 522 ÷ 2 = 964 261 + 0;
  • 964 261 ÷ 2 = 482 130 + 1;
  • 482 130 ÷ 2 = 241 065 + 0;
  • 241 065 ÷ 2 = 120 532 + 1;
  • 120 532 ÷ 2 = 60 266 + 0;
  • 60 266 ÷ 2 = 30 133 + 0;
  • 30 133 ÷ 2 = 15 066 + 1;
  • 15 066 ÷ 2 = 7 533 + 0;
  • 7 533 ÷ 2 = 3 766 + 1;
  • 3 766 ÷ 2 = 1 883 + 0;
  • 1 883 ÷ 2 = 941 + 1;
  • 941 ÷ 2 = 470 + 1;
  • 470 ÷ 2 = 235 + 0;
  • 235 ÷ 2 = 117 + 1;
  • 117 ÷ 2 = 58 + 1;
  • 58 ÷ 2 = 29 + 0;
  • 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.

1 011 101 110 909(10) = 1110 1011 0110 1010 0101 0010 1001 0010 0111 1101(2)

3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 40.

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, 40,

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 1 011 101 110 909(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:

1 011 101 110 909(10) = 0000 0000 0000 0000 0000 0000 1110 1011 0110 1010 0101 0010 1001 0010 0111 1101

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

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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