Convert 84 688 897 866 040 to a signed binary in two's complement representation, from a signed integer number in base 10 decimal system

84 688 897 866 040(10) to a signed binary 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;
  • 84 688 897 866 040 ÷ 2 = 42 344 448 933 020 + 0;
  • 42 344 448 933 020 ÷ 2 = 21 172 224 466 510 + 0;
  • 21 172 224 466 510 ÷ 2 = 10 586 112 233 255 + 0;
  • 10 586 112 233 255 ÷ 2 = 5 293 056 116 627 + 1;
  • 5 293 056 116 627 ÷ 2 = 2 646 528 058 313 + 1;
  • 2 646 528 058 313 ÷ 2 = 1 323 264 029 156 + 1;
  • 1 323 264 029 156 ÷ 2 = 661 632 014 578 + 0;
  • 661 632 014 578 ÷ 2 = 330 816 007 289 + 0;
  • 330 816 007 289 ÷ 2 = 165 408 003 644 + 1;
  • 165 408 003 644 ÷ 2 = 82 704 001 822 + 0;
  • 82 704 001 822 ÷ 2 = 41 352 000 911 + 0;
  • 41 352 000 911 ÷ 2 = 20 676 000 455 + 1;
  • 20 676 000 455 ÷ 2 = 10 338 000 227 + 1;
  • 10 338 000 227 ÷ 2 = 5 169 000 113 + 1;
  • 5 169 000 113 ÷ 2 = 2 584 500 056 + 1;
  • 2 584 500 056 ÷ 2 = 1 292 250 028 + 0;
  • 1 292 250 028 ÷ 2 = 646 125 014 + 0;
  • 646 125 014 ÷ 2 = 323 062 507 + 0;
  • 323 062 507 ÷ 2 = 161 531 253 + 1;
  • 161 531 253 ÷ 2 = 80 765 626 + 1;
  • 80 765 626 ÷ 2 = 40 382 813 + 0;
  • 40 382 813 ÷ 2 = 20 191 406 + 1;
  • 20 191 406 ÷ 2 = 10 095 703 + 0;
  • 10 095 703 ÷ 2 = 5 047 851 + 1;
  • 5 047 851 ÷ 2 = 2 523 925 + 1;
  • 2 523 925 ÷ 2 = 1 261 962 + 1;
  • 1 261 962 ÷ 2 = 630 981 + 0;
  • 630 981 ÷ 2 = 315 490 + 1;
  • 315 490 ÷ 2 = 157 745 + 0;
  • 157 745 ÷ 2 = 78 872 + 1;
  • 78 872 ÷ 2 = 39 436 + 0;
  • 39 436 ÷ 2 = 19 718 + 0;
  • 19 718 ÷ 2 = 9 859 + 0;
  • 9 859 ÷ 2 = 4 929 + 1;
  • 4 929 ÷ 2 = 2 464 + 1;
  • 2 464 ÷ 2 = 1 232 + 0;
  • 1 232 ÷ 2 = 616 + 0;
  • 616 ÷ 2 = 308 + 0;
  • 308 ÷ 2 = 154 + 0;
  • 154 ÷ 2 = 77 + 0;
  • 77 ÷ 2 = 38 + 1;
  • 38 ÷ 2 = 19 + 0;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 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.

84 688 897 866 040(10) = 100 1101 0000 0110 0010 1011 1010 1100 0111 1001 0011 1000(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 47.

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; ...

First bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

The least number that is:


a power of 2


and is larger than the actual length, 47,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


is: 64.


4. 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:

84 688 897 866 040(10) = 0000 0000 0000 0000 0100 1101 0000 0110 0010 1011 1010 1100 0111 1001 0011 1000


Number 84 688 897 866 040, a signed integer, converted from decimal system (base 10) to a signed binary two's complement representation:

84 688 897 866 040(10) = 0000 0000 0000 0000 0100 1101 0000 0110 0010 1011 1010 1100 0111 1001 0011 1000

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


More operations of this kind:

84 688 897 866 039 = ? | 84 688 897 866 041 = ?


Convert signed integer numbers from the decimal system (base ten) to signed binary two's complement representation

How to convert a base 10 signed integer number to signed binary in two's complement representation:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is equal to 0.

2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.

3) Construct the positive binary computer representation so that the first bit is 0.

4) Only if the initial number is negative, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).

5) Only if the initial number is negative, add 1 to the number at the previous point.

Latest signed integers converted from decimal system to binary two's complement representation

84,688,897,866,040 to signed binary two's complement = ? May 06 19:55 UTC (GMT)
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-398 to signed binary two's complement = ? May 06 19:55 UTC (GMT)
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15,433 to signed binary two's complement = ? May 06 19:54 UTC (GMT)
11,010,098 to signed binary two's complement = ? May 06 19:54 UTC (GMT)
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1,000,000,002 to signed binary two's complement = ? May 06 19:54 UTC (GMT)
47,656 to signed binary two's complement = ? May 06 19:54 UTC (GMT)
-566 to signed binary two's complement = ? May 06 19:54 UTC (GMT)
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All decimal integer numbers converted to signed binary two's complement representation

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