Convert 11 111 001 116 to signed binary, from a base 10 decimal system signed integer number

How to convert the signed integer in decimal system (in base 10):
11 111 001 116(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;
  • 11 111 001 116 ÷ 2 = 5 555 500 558 + 0;
  • 5 555 500 558 ÷ 2 = 2 777 750 279 + 0;
  • 2 777 750 279 ÷ 2 = 1 388 875 139 + 1;
  • 1 388 875 139 ÷ 2 = 694 437 569 + 1;
  • 694 437 569 ÷ 2 = 347 218 784 + 1;
  • 347 218 784 ÷ 2 = 173 609 392 + 0;
  • 173 609 392 ÷ 2 = 86 804 696 + 0;
  • 86 804 696 ÷ 2 = 43 402 348 + 0;
  • 43 402 348 ÷ 2 = 21 701 174 + 0;
  • 21 701 174 ÷ 2 = 10 850 587 + 0;
  • 10 850 587 ÷ 2 = 5 425 293 + 1;
  • 5 425 293 ÷ 2 = 2 712 646 + 1;
  • 2 712 646 ÷ 2 = 1 356 323 + 0;
  • 1 356 323 ÷ 2 = 678 161 + 1;
  • 678 161 ÷ 2 = 339 080 + 1;
  • 339 080 ÷ 2 = 169 540 + 0;
  • 169 540 ÷ 2 = 84 770 + 0;
  • 84 770 ÷ 2 = 42 385 + 0;
  • 42 385 ÷ 2 = 21 192 + 1;
  • 21 192 ÷ 2 = 10 596 + 0;
  • 10 596 ÷ 2 = 5 298 + 0;
  • 5 298 ÷ 2 = 2 649 + 0;
  • 2 649 ÷ 2 = 1 324 + 1;
  • 1 324 ÷ 2 = 662 + 0;
  • 662 ÷ 2 = 331 + 0;
  • 331 ÷ 2 = 165 + 1;
  • 165 ÷ 2 = 82 + 1;
  • 82 ÷ 2 = 41 + 0;
  • 41 ÷ 2 = 20 + 1;
  • 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.

11 111 001 116(10) = 10 1001 0110 0100 0100 0110 1100 0001 1100(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 34.

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, 34,


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:

11 111 001 116(10) = 0000 0000 0000 0000 0000 0000 0000 0010 1001 0110 0100 0100 0110 1100 0001 1100


Conclusion:

Number 11 111 001 116, a signed integer, converted from decimal system (base 10) to signed binary:

11 111 001 116(10) = 0000 0000 0000 0000 0000 0000 0000 0010 1001 0110 0100 0100 0110 1100 0001 1100

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:

11 111 001 115 = ? | Signed integer 11 111 001 117 = ?


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

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