Convert 1 122 334 455 667 738 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 1 122 334 455 667 738(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
1 122 334 455 667 738 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;
  • 1 122 334 455 667 738 ÷ 2 = 561 167 227 833 869 + 0;
  • 561 167 227 833 869 ÷ 2 = 280 583 613 916 934 + 1;
  • 280 583 613 916 934 ÷ 2 = 140 291 806 958 467 + 0;
  • 140 291 806 958 467 ÷ 2 = 70 145 903 479 233 + 1;
  • 70 145 903 479 233 ÷ 2 = 35 072 951 739 616 + 1;
  • 35 072 951 739 616 ÷ 2 = 17 536 475 869 808 + 0;
  • 17 536 475 869 808 ÷ 2 = 8 768 237 934 904 + 0;
  • 8 768 237 934 904 ÷ 2 = 4 384 118 967 452 + 0;
  • 4 384 118 967 452 ÷ 2 = 2 192 059 483 726 + 0;
  • 2 192 059 483 726 ÷ 2 = 1 096 029 741 863 + 0;
  • 1 096 029 741 863 ÷ 2 = 548 014 870 931 + 1;
  • 548 014 870 931 ÷ 2 = 274 007 435 465 + 1;
  • 274 007 435 465 ÷ 2 = 137 003 717 732 + 1;
  • 137 003 717 732 ÷ 2 = 68 501 858 866 + 0;
  • 68 501 858 866 ÷ 2 = 34 250 929 433 + 0;
  • 34 250 929 433 ÷ 2 = 17 125 464 716 + 1;
  • 17 125 464 716 ÷ 2 = 8 562 732 358 + 0;
  • 8 562 732 358 ÷ 2 = 4 281 366 179 + 0;
  • 4 281 366 179 ÷ 2 = 2 140 683 089 + 1;
  • 2 140 683 089 ÷ 2 = 1 070 341 544 + 1;
  • 1 070 341 544 ÷ 2 = 535 170 772 + 0;
  • 535 170 772 ÷ 2 = 267 585 386 + 0;
  • 267 585 386 ÷ 2 = 133 792 693 + 0;
  • 133 792 693 ÷ 2 = 66 896 346 + 1;
  • 66 896 346 ÷ 2 = 33 448 173 + 0;
  • 33 448 173 ÷ 2 = 16 724 086 + 1;
  • 16 724 086 ÷ 2 = 8 362 043 + 0;
  • 8 362 043 ÷ 2 = 4 181 021 + 1;
  • 4 181 021 ÷ 2 = 2 090 510 + 1;
  • 2 090 510 ÷ 2 = 1 045 255 + 0;
  • 1 045 255 ÷ 2 = 522 627 + 1;
  • 522 627 ÷ 2 = 261 313 + 1;
  • 261 313 ÷ 2 = 130 656 + 1;
  • 130 656 ÷ 2 = 65 328 + 0;
  • 65 328 ÷ 2 = 32 664 + 0;
  • 32 664 ÷ 2 = 16 332 + 0;
  • 16 332 ÷ 2 = 8 166 + 0;
  • 8 166 ÷ 2 = 4 083 + 0;
  • 4 083 ÷ 2 = 2 041 + 1;
  • 2 041 ÷ 2 = 1 020 + 1;
  • 1 020 ÷ 2 = 510 + 0;
  • 510 ÷ 2 = 255 + 0;
  • 255 ÷ 2 = 127 + 1;
  • 127 ÷ 2 = 63 + 1;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.

1 122 334 455 667 738(10) = 11 1111 1100 1100 0001 1101 1010 1000 1100 1001 1100 0001 1010(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 1 122 334 455 667 738(10) converted to signed binary in two's complement representation:

1 122 334 455 667 738(10) = 0000 0000 0000 0011 1111 1100 1100 0001 1101 1010 1000 1100 1001 1100 0001 1010

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