Convert 281 479 278 821 330 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 281 479 278 821 330(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
281 479 278 821 330 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;
  • 281 479 278 821 330 ÷ 2 = 140 739 639 410 665 + 0;
  • 140 739 639 410 665 ÷ 2 = 70 369 819 705 332 + 1;
  • 70 369 819 705 332 ÷ 2 = 35 184 909 852 666 + 0;
  • 35 184 909 852 666 ÷ 2 = 17 592 454 926 333 + 0;
  • 17 592 454 926 333 ÷ 2 = 8 796 227 463 166 + 1;
  • 8 796 227 463 166 ÷ 2 = 4 398 113 731 583 + 0;
  • 4 398 113 731 583 ÷ 2 = 2 199 056 865 791 + 1;
  • 2 199 056 865 791 ÷ 2 = 1 099 528 432 895 + 1;
  • 1 099 528 432 895 ÷ 2 = 549 764 216 447 + 1;
  • 549 764 216 447 ÷ 2 = 274 882 108 223 + 1;
  • 274 882 108 223 ÷ 2 = 137 441 054 111 + 1;
  • 137 441 054 111 ÷ 2 = 68 720 527 055 + 1;
  • 68 720 527 055 ÷ 2 = 34 360 263 527 + 1;
  • 34 360 263 527 ÷ 2 = 17 180 131 763 + 1;
  • 17 180 131 763 ÷ 2 = 8 590 065 881 + 1;
  • 8 590 065 881 ÷ 2 = 4 295 032 940 + 1;
  • 4 295 032 940 ÷ 2 = 2 147 516 470 + 0;
  • 2 147 516 470 ÷ 2 = 1 073 758 235 + 0;
  • 1 073 758 235 ÷ 2 = 536 879 117 + 1;
  • 536 879 117 ÷ 2 = 268 439 558 + 1;
  • 268 439 558 ÷ 2 = 134 219 779 + 0;
  • 134 219 779 ÷ 2 = 67 109 889 + 1;
  • 67 109 889 ÷ 2 = 33 554 944 + 1;
  • 33 554 944 ÷ 2 = 16 777 472 + 0;
  • 16 777 472 ÷ 2 = 8 388 736 + 0;
  • 8 388 736 ÷ 2 = 4 194 368 + 0;
  • 4 194 368 ÷ 2 = 2 097 184 + 0;
  • 2 097 184 ÷ 2 = 1 048 592 + 0;
  • 1 048 592 ÷ 2 = 524 296 + 0;
  • 524 296 ÷ 2 = 262 148 + 0;
  • 262 148 ÷ 2 = 131 074 + 0;
  • 131 074 ÷ 2 = 65 537 + 0;
  • 65 537 ÷ 2 = 32 768 + 1;
  • 32 768 ÷ 2 = 16 384 + 0;
  • 16 384 ÷ 2 = 8 192 + 0;
  • 8 192 ÷ 2 = 4 096 + 0;
  • 4 096 ÷ 2 = 2 048 + 0;
  • 2 048 ÷ 2 = 1 024 + 0;
  • 1 024 ÷ 2 = 512 + 0;
  • 512 ÷ 2 = 256 + 0;
  • 256 ÷ 2 = 128 + 0;
  • 128 ÷ 2 = 64 + 0;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 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.

281 479 278 821 330(10) = 1 0000 0000 0000 0001 0000 0000 0110 1100 1111 1111 1101 0010(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 49.

  • 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, 49,

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 281 479 278 821 330(10) converted to signed binary in two's complement representation:

281 479 278 821 330(10) = 0000 0000 0000 0001 0000 0000 0000 0001 0000 0000 0110 1100 1111 1111 1101 0010

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