Convert 1 011 000 011 110 107 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):
1 011 000 011 110 107(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;
  • 1 011 000 011 110 107 ÷ 2 = 505 500 005 555 053 + 1;
  • 505 500 005 555 053 ÷ 2 = 252 750 002 777 526 + 1;
  • 252 750 002 777 526 ÷ 2 = 126 375 001 388 763 + 0;
  • 126 375 001 388 763 ÷ 2 = 63 187 500 694 381 + 1;
  • 63 187 500 694 381 ÷ 2 = 31 593 750 347 190 + 1;
  • 31 593 750 347 190 ÷ 2 = 15 796 875 173 595 + 0;
  • 15 796 875 173 595 ÷ 2 = 7 898 437 586 797 + 1;
  • 7 898 437 586 797 ÷ 2 = 3 949 218 793 398 + 1;
  • 3 949 218 793 398 ÷ 2 = 1 974 609 396 699 + 0;
  • 1 974 609 396 699 ÷ 2 = 987 304 698 349 + 1;
  • 987 304 698 349 ÷ 2 = 493 652 349 174 + 1;
  • 493 652 349 174 ÷ 2 = 246 826 174 587 + 0;
  • 246 826 174 587 ÷ 2 = 123 413 087 293 + 1;
  • 123 413 087 293 ÷ 2 = 61 706 543 646 + 1;
  • 61 706 543 646 ÷ 2 = 30 853 271 823 + 0;
  • 30 853 271 823 ÷ 2 = 15 426 635 911 + 1;
  • 15 426 635 911 ÷ 2 = 7 713 317 955 + 1;
  • 7 713 317 955 ÷ 2 = 3 856 658 977 + 1;
  • 3 856 658 977 ÷ 2 = 1 928 329 488 + 1;
  • 1 928 329 488 ÷ 2 = 964 164 744 + 0;
  • 964 164 744 ÷ 2 = 482 082 372 + 0;
  • 482 082 372 ÷ 2 = 241 041 186 + 0;
  • 241 041 186 ÷ 2 = 120 520 593 + 0;
  • 120 520 593 ÷ 2 = 60 260 296 + 1;
  • 60 260 296 ÷ 2 = 30 130 148 + 0;
  • 30 130 148 ÷ 2 = 15 065 074 + 0;
  • 15 065 074 ÷ 2 = 7 532 537 + 0;
  • 7 532 537 ÷ 2 = 3 766 268 + 1;
  • 3 766 268 ÷ 2 = 1 883 134 + 0;
  • 1 883 134 ÷ 2 = 941 567 + 0;
  • 941 567 ÷ 2 = 470 783 + 1;
  • 470 783 ÷ 2 = 235 391 + 1;
  • 235 391 ÷ 2 = 117 695 + 1;
  • 117 695 ÷ 2 = 58 847 + 1;
  • 58 847 ÷ 2 = 29 423 + 1;
  • 29 423 ÷ 2 = 14 711 + 1;
  • 14 711 ÷ 2 = 7 355 + 1;
  • 7 355 ÷ 2 = 3 677 + 1;
  • 3 677 ÷ 2 = 1 838 + 1;
  • 1 838 ÷ 2 = 919 + 0;
  • 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.

1 011 000 011 110 107(10) = 11 1001 0111 0111 1111 1100 1000 1000 0111 1011 0110 1101 1011(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:

1 011 000 011 110 107(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 1000 1000 0111 1011 0110 1101 1011


Conclusion:

Number 1 011 000 011 110 107, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

1 011 000 011 110 107(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 1000 1000 0111 1011 0110 1101 1011

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


More operations of this kind:

1 011 000 011 110 106 = ? | 1 011 000 011 110 108 = ?


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