Convert -9 223 372 036 854 775 771 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

How to convert a signed integer in decimal system (in base 10):
-9 223 372 036 854 775 771(10)
to a signed binary one's complement representation

1. Start with the positive version of the number:

|-9 223 372 036 854 775 771| = 9 223 372 036 854 775 771

2. 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;
  • 9 223 372 036 854 775 771 ÷ 2 = 4 611 686 018 427 387 885 + 1;
  • 4 611 686 018 427 387 885 ÷ 2 = 2 305 843 009 213 693 942 + 1;
  • 2 305 843 009 213 693 942 ÷ 2 = 1 152 921 504 606 846 971 + 0;
  • 1 152 921 504 606 846 971 ÷ 2 = 576 460 752 303 423 485 + 1;
  • 576 460 752 303 423 485 ÷ 2 = 288 230 376 151 711 742 + 1;
  • 288 230 376 151 711 742 ÷ 2 = 144 115 188 075 855 871 + 0;
  • 144 115 188 075 855 871 ÷ 2 = 72 057 594 037 927 935 + 1;
  • 72 057 594 037 927 935 ÷ 2 = 36 028 797 018 963 967 + 1;
  • 36 028 797 018 963 967 ÷ 2 = 18 014 398 509 481 983 + 1;
  • 18 014 398 509 481 983 ÷ 2 = 9 007 199 254 740 991 + 1;
  • 9 007 199 254 740 991 ÷ 2 = 4 503 599 627 370 495 + 1;
  • 4 503 599 627 370 495 ÷ 2 = 2 251 799 813 685 247 + 1;
  • 2 251 799 813 685 247 ÷ 2 = 1 125 899 906 842 623 + 1;
  • 1 125 899 906 842 623 ÷ 2 = 562 949 953 421 311 + 1;
  • 562 949 953 421 311 ÷ 2 = 281 474 976 710 655 + 1;
  • 281 474 976 710 655 ÷ 2 = 140 737 488 355 327 + 1;
  • 140 737 488 355 327 ÷ 2 = 70 368 744 177 663 + 1;
  • 70 368 744 177 663 ÷ 2 = 35 184 372 088 831 + 1;
  • 35 184 372 088 831 ÷ 2 = 17 592 186 044 415 + 1;
  • 17 592 186 044 415 ÷ 2 = 8 796 093 022 207 + 1;
  • 8 796 093 022 207 ÷ 2 = 4 398 046 511 103 + 1;
  • 4 398 046 511 103 ÷ 2 = 2 199 023 255 551 + 1;
  • 2 199 023 255 551 ÷ 2 = 1 099 511 627 775 + 1;
  • 1 099 511 627 775 ÷ 2 = 549 755 813 887 + 1;
  • 549 755 813 887 ÷ 2 = 274 877 906 943 + 1;
  • 274 877 906 943 ÷ 2 = 137 438 953 471 + 1;
  • 137 438 953 471 ÷ 2 = 68 719 476 735 + 1;
  • 68 719 476 735 ÷ 2 = 34 359 738 367 + 1;
  • 34 359 738 367 ÷ 2 = 17 179 869 183 + 1;
  • 17 179 869 183 ÷ 2 = 8 589 934 591 + 1;
  • 8 589 934 591 ÷ 2 = 4 294 967 295 + 1;
  • 4 294 967 295 ÷ 2 = 2 147 483 647 + 1;
  • 2 147 483 647 ÷ 2 = 1 073 741 823 + 1;
  • 1 073 741 823 ÷ 2 = 536 870 911 + 1;
  • 536 870 911 ÷ 2 = 268 435 455 + 1;
  • 268 435 455 ÷ 2 = 134 217 727 + 1;
  • 134 217 727 ÷ 2 = 67 108 863 + 1;
  • 67 108 863 ÷ 2 = 33 554 431 + 1;
  • 33 554 431 ÷ 2 = 16 777 215 + 1;
  • 16 777 215 ÷ 2 = 8 388 607 + 1;
  • 8 388 607 ÷ 2 = 4 194 303 + 1;
  • 4 194 303 ÷ 2 = 2 097 151 + 1;
  • 2 097 151 ÷ 2 = 1 048 575 + 1;
  • 1 048 575 ÷ 2 = 524 287 + 1;
  • 524 287 ÷ 2 = 262 143 + 1;
  • 262 143 ÷ 2 = 131 071 + 1;
  • 131 071 ÷ 2 = 65 535 + 1;
  • 65 535 ÷ 2 = 32 767 + 1;
  • 32 767 ÷ 2 = 16 383 + 1;
  • 16 383 ÷ 2 = 8 191 + 1;
  • 8 191 ÷ 2 = 4 095 + 1;
  • 4 095 ÷ 2 = 2 047 + 1;
  • 2 047 ÷ 2 = 1 023 + 1;
  • 1 023 ÷ 2 = 511 + 1;
  • 511 ÷ 2 = 255 + 1;
  • 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;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

9 223 372 036 854 775 771(10) = 111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1101 1011(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 63.

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, 63,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


is: 64.


5. 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:

9 223 372 036 854 775 771(10) = 0111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1101 1011


6. Get the negative integer number representation:

To get the negative integer number representation on 64 bits (8 Bytes),


signed binary one's complement,


replace all the bits on 0 with 1s


and all the bits set on 1 with 0s


(reverse the digits, flip the digits)


!(0111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1101 1011) =


1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0100


Conclusion:

Number -9 223 372 036 854 775 771, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

-9 223 372 036 854 775 771(10) = 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0100

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


More operations of this kind:

-9 223 372 036 854 775 772 = ? | -9 223 372 036 854 775 770 = ?


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

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

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

Latest signed integer numbers converted from decimal system to signed binary in one's complement representation

-9,223,372,036,854,775,771 to signed binary one's complement = ? Jan 24 11:52 UTC (GMT)
-72 to signed binary one's complement = ? Jan 24 11:50 UTC (GMT)
-572 to signed binary one's complement = ? Jan 24 11:49 UTC (GMT)
278 to signed binary one's complement = ? Jan 24 11:49 UTC (GMT)
867,874,990 to signed binary one's complement = ? Jan 24 11:48 UTC (GMT)
111,111,111,111,122 to signed binary one's complement = ? Jan 24 11:48 UTC (GMT)
-2,147,482,602 to signed binary one's complement = ? Jan 24 11:47 UTC (GMT)
-8,032 to signed binary one's complement = ? Jan 24 11:45 UTC (GMT)
70,927 to signed binary one's complement = ? Jan 24 11:45 UTC (GMT)
1,101,100,101,110,108 to signed binary one's complement = ? Jan 24 11:45 UTC (GMT)
1,488 to signed binary one's complement = ? Jan 24 11:45 UTC (GMT)
657,089 to signed binary one's complement = ? Jan 24 11:45 UTC (GMT)
-10,486 to signed binary one's complement = ? Jan 24 11:45 UTC (GMT)
All decimal integer numbers converted to signed binary one's complement representation

How to convert signed integers from the decimal system to signed binary in one's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in one'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 that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to 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, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always 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 '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 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:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110