Convert 1 011 111 010 100 106 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):
1 011 111 010 100 106(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;
  • 1 011 111 010 100 106 ÷ 2 = 505 555 505 050 053 + 0;
  • 505 555 505 050 053 ÷ 2 = 252 777 752 525 026 + 1;
  • 252 777 752 525 026 ÷ 2 = 126 388 876 262 513 + 0;
  • 126 388 876 262 513 ÷ 2 = 63 194 438 131 256 + 1;
  • 63 194 438 131 256 ÷ 2 = 31 597 219 065 628 + 0;
  • 31 597 219 065 628 ÷ 2 = 15 798 609 532 814 + 0;
  • 15 798 609 532 814 ÷ 2 = 7 899 304 766 407 + 0;
  • 7 899 304 766 407 ÷ 2 = 3 949 652 383 203 + 1;
  • 3 949 652 383 203 ÷ 2 = 1 974 826 191 601 + 1;
  • 1 974 826 191 601 ÷ 2 = 987 413 095 800 + 1;
  • 987 413 095 800 ÷ 2 = 493 706 547 900 + 0;
  • 493 706 547 900 ÷ 2 = 246 853 273 950 + 0;
  • 246 853 273 950 ÷ 2 = 123 426 636 975 + 0;
  • 123 426 636 975 ÷ 2 = 61 713 318 487 + 1;
  • 61 713 318 487 ÷ 2 = 30 856 659 243 + 1;
  • 30 856 659 243 ÷ 2 = 15 428 329 621 + 1;
  • 15 428 329 621 ÷ 2 = 7 714 164 810 + 1;
  • 7 714 164 810 ÷ 2 = 3 857 082 405 + 0;
  • 3 857 082 405 ÷ 2 = 1 928 541 202 + 1;
  • 1 928 541 202 ÷ 2 = 964 270 601 + 0;
  • 964 270 601 ÷ 2 = 482 135 300 + 1;
  • 482 135 300 ÷ 2 = 241 067 650 + 0;
  • 241 067 650 ÷ 2 = 120 533 825 + 0;
  • 120 533 825 ÷ 2 = 60 266 912 + 1;
  • 60 266 912 ÷ 2 = 30 133 456 + 0;
  • 30 133 456 ÷ 2 = 15 066 728 + 0;
  • 15 066 728 ÷ 2 = 7 533 364 + 0;
  • 7 533 364 ÷ 2 = 3 766 682 + 0;
  • 3 766 682 ÷ 2 = 1 883 341 + 0;
  • 1 883 341 ÷ 2 = 941 670 + 1;
  • 941 670 ÷ 2 = 470 835 + 0;
  • 470 835 ÷ 2 = 235 417 + 1;
  • 235 417 ÷ 2 = 117 708 + 1;
  • 117 708 ÷ 2 = 58 854 + 0;
  • 58 854 ÷ 2 = 29 427 + 0;
  • 29 427 ÷ 2 = 14 713 + 1;
  • 14 713 ÷ 2 = 7 356 + 1;
  • 7 356 ÷ 2 = 3 678 + 0;
  • 3 678 ÷ 2 = 1 839 + 0;
  • 1 839 ÷ 2 = 919 + 1;
  • 919 ÷ 2 = 459 + 1;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.

1 011 111 010 100 106(10) = 11 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1000 1010(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 50.

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, 50,


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:

1 011 111 010 100 106(10) = 0000 0000 0000 0011 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1000 1010


Conclusion:

Number 1 011 111 010 100 106, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

1 011 111 010 100 106(10) = 0000 0000 0000 0011 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1000 1010

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


More operations of this kind:

1 011 111 010 100 105 = ? | 1 011 111 010 100 107 = ?


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

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