Convert 600 520 203 909 999 828 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 600 520 203 909 999 828(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
600 520 203 909 999 828 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;
  • 600 520 203 909 999 828 ÷ 2 = 300 260 101 954 999 914 + 0;
  • 300 260 101 954 999 914 ÷ 2 = 150 130 050 977 499 957 + 0;
  • 150 130 050 977 499 957 ÷ 2 = 75 065 025 488 749 978 + 1;
  • 75 065 025 488 749 978 ÷ 2 = 37 532 512 744 374 989 + 0;
  • 37 532 512 744 374 989 ÷ 2 = 18 766 256 372 187 494 + 1;
  • 18 766 256 372 187 494 ÷ 2 = 9 383 128 186 093 747 + 0;
  • 9 383 128 186 093 747 ÷ 2 = 4 691 564 093 046 873 + 1;
  • 4 691 564 093 046 873 ÷ 2 = 2 345 782 046 523 436 + 1;
  • 2 345 782 046 523 436 ÷ 2 = 1 172 891 023 261 718 + 0;
  • 1 172 891 023 261 718 ÷ 2 = 586 445 511 630 859 + 0;
  • 586 445 511 630 859 ÷ 2 = 293 222 755 815 429 + 1;
  • 293 222 755 815 429 ÷ 2 = 146 611 377 907 714 + 1;
  • 146 611 377 907 714 ÷ 2 = 73 305 688 953 857 + 0;
  • 73 305 688 953 857 ÷ 2 = 36 652 844 476 928 + 1;
  • 36 652 844 476 928 ÷ 2 = 18 326 422 238 464 + 0;
  • 18 326 422 238 464 ÷ 2 = 9 163 211 119 232 + 0;
  • 9 163 211 119 232 ÷ 2 = 4 581 605 559 616 + 0;
  • 4 581 605 559 616 ÷ 2 = 2 290 802 779 808 + 0;
  • 2 290 802 779 808 ÷ 2 = 1 145 401 389 904 + 0;
  • 1 145 401 389 904 ÷ 2 = 572 700 694 952 + 0;
  • 572 700 694 952 ÷ 2 = 286 350 347 476 + 0;
  • 286 350 347 476 ÷ 2 = 143 175 173 738 + 0;
  • 143 175 173 738 ÷ 2 = 71 587 586 869 + 0;
  • 71 587 586 869 ÷ 2 = 35 793 793 434 + 1;
  • 35 793 793 434 ÷ 2 = 17 896 896 717 + 0;
  • 17 896 896 717 ÷ 2 = 8 948 448 358 + 1;
  • 8 948 448 358 ÷ 2 = 4 474 224 179 + 0;
  • 4 474 224 179 ÷ 2 = 2 237 112 089 + 1;
  • 2 237 112 089 ÷ 2 = 1 118 556 044 + 1;
  • 1 118 556 044 ÷ 2 = 559 278 022 + 0;
  • 559 278 022 ÷ 2 = 279 639 011 + 0;
  • 279 639 011 ÷ 2 = 139 819 505 + 1;
  • 139 819 505 ÷ 2 = 69 909 752 + 1;
  • 69 909 752 ÷ 2 = 34 954 876 + 0;
  • 34 954 876 ÷ 2 = 17 477 438 + 0;
  • 17 477 438 ÷ 2 = 8 738 719 + 0;
  • 8 738 719 ÷ 2 = 4 369 359 + 1;
  • 4 369 359 ÷ 2 = 2 184 679 + 1;
  • 2 184 679 ÷ 2 = 1 092 339 + 1;
  • 1 092 339 ÷ 2 = 546 169 + 1;
  • 546 169 ÷ 2 = 273 084 + 1;
  • 273 084 ÷ 2 = 136 542 + 0;
  • 136 542 ÷ 2 = 68 271 + 0;
  • 68 271 ÷ 2 = 34 135 + 1;
  • 34 135 ÷ 2 = 17 067 + 1;
  • 17 067 ÷ 2 = 8 533 + 1;
  • 8 533 ÷ 2 = 4 266 + 1;
  • 4 266 ÷ 2 = 2 133 + 0;
  • 2 133 ÷ 2 = 1 066 + 1;
  • 1 066 ÷ 2 = 533 + 0;
  • 533 ÷ 2 = 266 + 1;
  • 266 ÷ 2 = 133 + 0;
  • 133 ÷ 2 = 66 + 1;
  • 66 ÷ 2 = 33 + 0;
  • 33 ÷ 2 = 16 + 1;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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.

600 520 203 909 999 828(10) = 1000 0101 0101 0111 1001 1111 0001 1001 1010 1000 0000 0010 1100 1101 0100(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 60.

  • 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, 60,

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 600 520 203 909 999 828(10) converted to signed binary in two's complement representation:

600 520 203 909 999 828(10) = 0000 1000 0101 0101 0111 1001 1111 0001 1001 1010 1000 0000 0010 1100 1101 0100

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