Convert 1 011 100 109 999 611 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 1 011 100 109 999 611(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
1 011 100 109 999 611 to a signed binary in two's (2's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

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;
  • 1 011 100 109 999 611 ÷ 2 = 505 550 054 999 805 + 1;
  • 505 550 054 999 805 ÷ 2 = 252 775 027 499 902 + 1;
  • 252 775 027 499 902 ÷ 2 = 126 387 513 749 951 + 0;
  • 126 387 513 749 951 ÷ 2 = 63 193 756 874 975 + 1;
  • 63 193 756 874 975 ÷ 2 = 31 596 878 437 487 + 1;
  • 31 596 878 437 487 ÷ 2 = 15 798 439 218 743 + 1;
  • 15 798 439 218 743 ÷ 2 = 7 899 219 609 371 + 1;
  • 7 899 219 609 371 ÷ 2 = 3 949 609 804 685 + 1;
  • 3 949 609 804 685 ÷ 2 = 1 974 804 902 342 + 1;
  • 1 974 804 902 342 ÷ 2 = 987 402 451 171 + 0;
  • 987 402 451 171 ÷ 2 = 493 701 225 585 + 1;
  • 493 701 225 585 ÷ 2 = 246 850 612 792 + 1;
  • 246 850 612 792 ÷ 2 = 123 425 306 396 + 0;
  • 123 425 306 396 ÷ 2 = 61 712 653 198 + 0;
  • 61 712 653 198 ÷ 2 = 30 856 326 599 + 0;
  • 30 856 326 599 ÷ 2 = 15 428 163 299 + 1;
  • 15 428 163 299 ÷ 2 = 7 714 081 649 + 1;
  • 7 714 081 649 ÷ 2 = 3 857 040 824 + 1;
  • 3 857 040 824 ÷ 2 = 1 928 520 412 + 0;
  • 1 928 520 412 ÷ 2 = 964 260 206 + 0;
  • 964 260 206 ÷ 2 = 482 130 103 + 0;
  • 482 130 103 ÷ 2 = 241 065 051 + 1;
  • 241 065 051 ÷ 2 = 120 532 525 + 1;
  • 120 532 525 ÷ 2 = 60 266 262 + 1;
  • 60 266 262 ÷ 2 = 30 133 131 + 0;
  • 30 133 131 ÷ 2 = 15 066 565 + 1;
  • 15 066 565 ÷ 2 = 7 533 282 + 1;
  • 7 533 282 ÷ 2 = 3 766 641 + 0;
  • 3 766 641 ÷ 2 = 1 883 320 + 1;
  • 1 883 320 ÷ 2 = 941 660 + 0;
  • 941 660 ÷ 2 = 470 830 + 0;
  • 470 830 ÷ 2 = 235 415 + 0;
  • 235 415 ÷ 2 = 117 707 + 1;
  • 117 707 ÷ 2 = 58 853 + 1;
  • 58 853 ÷ 2 = 29 426 + 1;
  • 29 426 ÷ 2 = 14 713 + 0;
  • 14 713 ÷ 2 = 7 356 + 1;
  • 7 356 ÷ 2 = 3 678 + 0;
  • 3 678 ÷ 2 = 1 839 + 0;
  • 1 839 ÷ 2 = 919 + 1;
  • 919 ÷ 2 = 459 + 1;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 28 ÷ 2 = 14 + 0;
  • 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.

1 011 100 109 999 611(10) = 11 1001 0111 1001 0111 0001 0110 1110 0011 1000 1101 1111 1011(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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, 50,

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.


Decimal Number 1 011 100 109 999 611(10) converted to signed binary in two's complement representation:

1 011 100 109 999 611(10) = 0000 0000 0000 0011 1001 0111 1001 0111 0001 0110 1110 0011 1000 1101 1111 1011

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