Convert 1 364 098 225 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):
1 364 098 225(10)
to a signed binary one'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;
  • 1 364 098 225 ÷ 2 = 682 049 112 + 1;
  • 682 049 112 ÷ 2 = 341 024 556 + 0;
  • 341 024 556 ÷ 2 = 170 512 278 + 0;
  • 170 512 278 ÷ 2 = 85 256 139 + 0;
  • 85 256 139 ÷ 2 = 42 628 069 + 1;
  • 42 628 069 ÷ 2 = 21 314 034 + 1;
  • 21 314 034 ÷ 2 = 10 657 017 + 0;
  • 10 657 017 ÷ 2 = 5 328 508 + 1;
  • 5 328 508 ÷ 2 = 2 664 254 + 0;
  • 2 664 254 ÷ 2 = 1 332 127 + 0;
  • 1 332 127 ÷ 2 = 666 063 + 1;
  • 666 063 ÷ 2 = 333 031 + 1;
  • 333 031 ÷ 2 = 166 515 + 1;
  • 166 515 ÷ 2 = 83 257 + 1;
  • 83 257 ÷ 2 = 41 628 + 1;
  • 41 628 ÷ 2 = 20 814 + 0;
  • 20 814 ÷ 2 = 10 407 + 0;
  • 10 407 ÷ 2 = 5 203 + 1;
  • 5 203 ÷ 2 = 2 601 + 1;
  • 2 601 ÷ 2 = 1 300 + 1;
  • 1 300 ÷ 2 = 650 + 0;
  • 650 ÷ 2 = 325 + 0;
  • 325 ÷ 2 = 162 + 1;
  • 162 ÷ 2 = 81 + 0;
  • 81 ÷ 2 = 40 + 1;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 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.

1 364 098 225(10) = 101 0001 0100 1110 0111 1100 1011 0001(2)


3. 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.


4. 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:

1 364 098 225(10) = 0101 0001 0100 1110 0111 1100 1011 0001


Conclusion:

Number 1 364 098 225, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

1 364 098 225(10) = 0101 0001 0100 1110 0111 1100 1011 0001

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


More operations of this kind:

1 364 098 224 = ? | 1 364 098 226 = ?


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

1,364,098,225 to signed binary one's complement = ? Jan 26 17:11 UTC (GMT)
-11,010,095 to signed binary one's complement = ? Jan 26 17:11 UTC (GMT)
22,037 to signed binary one's complement = ? Jan 26 17:11 UTC (GMT)
-120,510 to signed binary one's complement = ? Jan 26 17:10 UTC (GMT)
-173,351,180 to signed binary one's complement = ? Jan 26 17:10 UTC (GMT)
-668 to signed binary one's complement = ? Jan 26 17:10 UTC (GMT)
-7,566 to signed binary one's complement = ? Jan 26 17:09 UTC (GMT)
564,564,841 to signed binary one's complement = ? Jan 26 17:09 UTC (GMT)
496,916,632,435,730,669 to signed binary one's complement = ? Jan 26 17:09 UTC (GMT)
4,690 to signed binary one's complement = ? Jan 26 17:08 UTC (GMT)
548 to signed binary one's complement = ? Jan 26 17:07 UTC (GMT)
89,998 to signed binary one's complement = ? Jan 26 17:06 UTC (GMT)
4,940 to signed binary one's complement = ? Jan 26 17:06 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