Convert -2 033 506 870 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):
-2 033 506 870(10)
to a signed binary one's complement representation

1. Start with the positive version of the number:

|-2 033 506 870| = 2 033 506 870

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;
  • 2 033 506 870 ÷ 2 = 1 016 753 435 + 0;
  • 1 016 753 435 ÷ 2 = 508 376 717 + 1;
  • 508 376 717 ÷ 2 = 254 188 358 + 1;
  • 254 188 358 ÷ 2 = 127 094 179 + 0;
  • 127 094 179 ÷ 2 = 63 547 089 + 1;
  • 63 547 089 ÷ 2 = 31 773 544 + 1;
  • 31 773 544 ÷ 2 = 15 886 772 + 0;
  • 15 886 772 ÷ 2 = 7 943 386 + 0;
  • 7 943 386 ÷ 2 = 3 971 693 + 0;
  • 3 971 693 ÷ 2 = 1 985 846 + 1;
  • 1 985 846 ÷ 2 = 992 923 + 0;
  • 992 923 ÷ 2 = 496 461 + 1;
  • 496 461 ÷ 2 = 248 230 + 1;
  • 248 230 ÷ 2 = 124 115 + 0;
  • 124 115 ÷ 2 = 62 057 + 1;
  • 62 057 ÷ 2 = 31 028 + 1;
  • 31 028 ÷ 2 = 15 514 + 0;
  • 15 514 ÷ 2 = 7 757 + 0;
  • 7 757 ÷ 2 = 3 878 + 1;
  • 3 878 ÷ 2 = 1 939 + 0;
  • 1 939 ÷ 2 = 969 + 1;
  • 969 ÷ 2 = 484 + 1;
  • 484 ÷ 2 = 242 + 0;
  • 242 ÷ 2 = 121 + 0;
  • 121 ÷ 2 = 60 + 1;
  • 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:

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

2 033 506 870(10) = 111 1001 0011 0100 1101 1010 0011 0110(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 31.

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, 31,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


is: 32.


5. Positive binary computer representation on 32 bits (4 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:

2 033 506 870(10) = 0111 1001 0011 0100 1101 1010 0011 0110


6. Get the negative integer number representation:

To get the negative integer number representation on 32 bits (4 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 1001 0011 0100 1101 1010 0011 0110) =


1000 0110 1100 1011 0010 0101 1100 1001


Conclusion:

Number -2 033 506 870, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

-2 033 506 870(10) = 1000 0110 1100 1011 0010 0101 1100 1001

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


More operations of this kind:

-2 033 506 871 = ? | -2 033 506 869 = ?


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

-2,033,506,870 to signed binary one's complement = ? Jan 16 05:08 UTC (GMT)
22,583 to signed binary one's complement = ? Jan 16 05:07 UTC (GMT)
22,598 to signed binary one's complement = ? Jan 16 05:06 UTC (GMT)
38,525 to signed binary one's complement = ? Jan 16 05:05 UTC (GMT)
-520 to signed binary one's complement = ? Jan 16 05:04 UTC (GMT)
32,765 to signed binary one's complement = ? Jan 16 05:03 UTC (GMT)
-1,000,005 to signed binary one's complement = ? Jan 16 05:02 UTC (GMT)
10,001,104 to signed binary one's complement = ? Jan 16 04:58 UTC (GMT)
354 to signed binary one's complement = ? Jan 16 04:57 UTC (GMT)
-267 to signed binary one's complement = ? Jan 16 04:57 UTC (GMT)
4,234,327 to signed binary one's complement = ? Jan 16 04:56 UTC (GMT)
1,010,101,101,010,000 to signed binary one's complement = ? Jan 16 04:55 UTC (GMT)
-419 to signed binary one's complement = ? Jan 16 04:54 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