Convert 1 133 903 870 to signed binary, from a base 10 decimal system signed integer number

How to convert the signed integer in decimal system (in base 10):
1 133 903 870(10)
to a signed binary

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;
  • 1 133 903 870 ÷ 2 = 566 951 935 + 0;
  • 566 951 935 ÷ 2 = 283 475 967 + 1;
  • 283 475 967 ÷ 2 = 141 737 983 + 1;
  • 141 737 983 ÷ 2 = 70 868 991 + 1;
  • 70 868 991 ÷ 2 = 35 434 495 + 1;
  • 35 434 495 ÷ 2 = 17 717 247 + 1;
  • 17 717 247 ÷ 2 = 8 858 623 + 1;
  • 8 858 623 ÷ 2 = 4 429 311 + 1;
  • 4 429 311 ÷ 2 = 2 214 655 + 1;
  • 2 214 655 ÷ 2 = 1 107 327 + 1;
  • 1 107 327 ÷ 2 = 553 663 + 1;
  • 553 663 ÷ 2 = 276 831 + 1;
  • 276 831 ÷ 2 = 138 415 + 1;
  • 138 415 ÷ 2 = 69 207 + 1;
  • 69 207 ÷ 2 = 34 603 + 1;
  • 34 603 ÷ 2 = 17 301 + 1;
  • 17 301 ÷ 2 = 8 650 + 1;
  • 8 650 ÷ 2 = 4 325 + 0;
  • 4 325 ÷ 2 = 2 162 + 1;
  • 2 162 ÷ 2 = 1 081 + 0;
  • 1 081 ÷ 2 = 540 + 1;
  • 540 ÷ 2 = 270 + 0;
  • 270 ÷ 2 = 135 + 0;
  • 135 ÷ 2 = 67 + 1;
  • 67 ÷ 2 = 33 + 1;
  • 33 ÷ 2 = 16 + 1;
  • 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.

1 133 903 870(10) = 100 0011 1001 0101 1111 1111 1111 1110(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) is reserved for the sign:
0 = positive integer number, 1 = negative integer number

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:

1 133 903 870(10) = 0100 0011 1001 0101 1111 1111 1111 1110


Conclusion:

Number 1 133 903 870, a signed integer, converted from decimal system (base 10) to signed binary:

1 133 903 870(10) = 0100 0011 1001 0101 1111 1111 1111 1110

First bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number

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


More operations of this kind:

1 133 903 869 = ? | Signed integer 1 133 903 871 = ?


Convert signed integer numbers from the decimal system (base ten) to signed binary

How to convert a base 10 signed integer number to signed binary:

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, change the first bit (the leftmost), from 0 to 1. The leftmost bit is reserved for the sign, 1 = negative, 0 = positive.

Latest signed integer numbers in decimal (base ten) converted to signed binary

1,133,903,870 to signed binary = ? Jan 21 02:41 UTC (GMT)
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1,000,011,011,010 to signed binary = ? Jan 21 02:40 UTC (GMT)
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565 to signed binary = ? Jan 21 02:40 UTC (GMT)
3,669 to signed binary = ? Jan 21 02:40 UTC (GMT)
-57 to signed binary = ? Jan 21 02:40 UTC (GMT)
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11,111,002 to signed binary = ? Jan 21 02:39 UTC (GMT)
1,011,011,111 to signed binary = ? Jan 21 02:39 UTC (GMT)
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All decimal positive integers converted to signed binary

How to convert signed integers from decimal system to binary code system

Follow the steps below to convert a signed base ten integer number to signed binary:

  • 1. In a signed binary, first bit (the leftmost) is reserved for sign: 0 = positive integer number, 1 = positive integer number. If the number to be converted is negative, start with its positive version.
  • 2. Divide repeatedly by 2 the positive integer number keeping track of each remainder. STOP when 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 have a length of 4, 8, 16, 32, 64, ... bits (power of 2) - if needed, fill in extra '0' bits in front of the base 2 number (to the left), up to the right length; this way the first bit (the leftmost one) is always '0', as for a positive representation.
  • 5. To get the negative reprezentation of the number, simply switch the first bit (the leftmost one), from '0' to '1'.

Example: convert the negative number -63 from decimal system (base ten) to signed binary code system:

  • 1. Start with the positive version of the number: |-63| = 63;
  • 2. Divide repeatedly 63 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder
    • 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, by taking all the remainders starting from the bottom of the list constructed above:
    63(10) = 11 1111(2)
  • 4. The actual length of base 2 representation number is 6, so the positive binary computer representation length of the signed binary will take in this case 8 bits (the least power of 2 higher than 6) - add extra '0's in front (to the left), up to the required length; this way the first bit (the leftmost one) is to be '0', as for a positive number:
    63(10) = 0011 1111(2)
  • 5. To get the negative integer number representation simply change the first bit (the leftmost), from '0' to '1':
    -63(10) = 1011 1111
  • Number -63(10), signed integer, converted from decimal system (base 10) to signed binary = 1011 1111