Integer as Two's Complement Binary: Number 1 011 001 100 947 Converted and Written as a Signed Binary in Two's Complement Representation

Integer number 1 011 001 100 947(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;
  • 1 011 001 100 947 ÷ 2 = 505 500 550 473 + 1;
  • 505 500 550 473 ÷ 2 = 252 750 275 236 + 1;
  • 252 750 275 236 ÷ 2 = 126 375 137 618 + 0;
  • 126 375 137 618 ÷ 2 = 63 187 568 809 + 0;
  • 63 187 568 809 ÷ 2 = 31 593 784 404 + 1;
  • 31 593 784 404 ÷ 2 = 15 796 892 202 + 0;
  • 15 796 892 202 ÷ 2 = 7 898 446 101 + 0;
  • 7 898 446 101 ÷ 2 = 3 949 223 050 + 1;
  • 3 949 223 050 ÷ 2 = 1 974 611 525 + 0;
  • 1 974 611 525 ÷ 2 = 987 305 762 + 1;
  • 987 305 762 ÷ 2 = 493 652 881 + 0;
  • 493 652 881 ÷ 2 = 246 826 440 + 1;
  • 246 826 440 ÷ 2 = 123 413 220 + 0;
  • 123 413 220 ÷ 2 = 61 706 610 + 0;
  • 61 706 610 ÷ 2 = 30 853 305 + 0;
  • 30 853 305 ÷ 2 = 15 426 652 + 1;
  • 15 426 652 ÷ 2 = 7 713 326 + 0;
  • 7 713 326 ÷ 2 = 3 856 663 + 0;
  • 3 856 663 ÷ 2 = 1 928 331 + 1;
  • 1 928 331 ÷ 2 = 964 165 + 1;
  • 964 165 ÷ 2 = 482 082 + 1;
  • 482 082 ÷ 2 = 241 041 + 0;
  • 241 041 ÷ 2 = 120 520 + 1;
  • 120 520 ÷ 2 = 60 260 + 0;
  • 60 260 ÷ 2 = 30 130 + 0;
  • 30 130 ÷ 2 = 15 065 + 0;
  • 15 065 ÷ 2 = 7 532 + 1;
  • 7 532 ÷ 2 = 3 766 + 0;
  • 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.

1 011 001 100 947(10) = 1110 1011 0110 0100 0101 1100 1000 1010 1001 0011(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 1 011 001 100 947(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:

1 011 001 100 947(10) = 0000 0000 0000 0000 0000 0000 1110 1011 0110 0100 0101 1100 1000 1010 1001 0011

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

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