Convert 1 011 110 100 101 011 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

1 011 110 100 101 011(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;
  • 1 011 110 100 101 011 ÷ 2 = 505 555 050 050 505 + 1;
  • 505 555 050 050 505 ÷ 2 = 252 777 525 025 252 + 1;
  • 252 777 525 025 252 ÷ 2 = 126 388 762 512 626 + 0;
  • 126 388 762 512 626 ÷ 2 = 63 194 381 256 313 + 0;
  • 63 194 381 256 313 ÷ 2 = 31 597 190 628 156 + 1;
  • 31 597 190 628 156 ÷ 2 = 15 798 595 314 078 + 0;
  • 15 798 595 314 078 ÷ 2 = 7 899 297 657 039 + 0;
  • 7 899 297 657 039 ÷ 2 = 3 949 648 828 519 + 1;
  • 3 949 648 828 519 ÷ 2 = 1 974 824 414 259 + 1;
  • 1 974 824 414 259 ÷ 2 = 987 412 207 129 + 1;
  • 987 412 207 129 ÷ 2 = 493 706 103 564 + 1;
  • 493 706 103 564 ÷ 2 = 246 853 051 782 + 0;
  • 246 853 051 782 ÷ 2 = 123 426 525 891 + 0;
  • 123 426 525 891 ÷ 2 = 61 713 262 945 + 1;
  • 61 713 262 945 ÷ 2 = 30 856 631 472 + 1;
  • 30 856 631 472 ÷ 2 = 15 428 315 736 + 0;
  • 15 428 315 736 ÷ 2 = 7 714 157 868 + 0;
  • 7 714 157 868 ÷ 2 = 3 857 078 934 + 0;
  • 3 857 078 934 ÷ 2 = 1 928 539 467 + 0;
  • 1 928 539 467 ÷ 2 = 964 269 733 + 1;
  • 964 269 733 ÷ 2 = 482 134 866 + 1;
  • 482 134 866 ÷ 2 = 241 067 433 + 0;
  • 241 067 433 ÷ 2 = 120 533 716 + 1;
  • 120 533 716 ÷ 2 = 60 266 858 + 0;
  • 60 266 858 ÷ 2 = 30 133 429 + 0;
  • 30 133 429 ÷ 2 = 15 066 714 + 1;
  • 15 066 714 ÷ 2 = 7 533 357 + 0;
  • 7 533 357 ÷ 2 = 3 766 678 + 1;
  • 3 766 678 ÷ 2 = 1 883 339 + 0;
  • 1 883 339 ÷ 2 = 941 669 + 1;
  • 941 669 ÷ 2 = 470 834 + 1;
  • 470 834 ÷ 2 = 235 417 + 0;
  • 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.

1 011 110 100 101 011(10) = 11 1001 0111 1001 1001 0110 1010 0101 1000 0110 0111 1001 0011(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:

1 011 110 100 101 011(10) = 0000 0000 0000 0011 1001 0111 1001 1001 0110 1010 0101 1000 0110 0111 1001 0011


Number 1 011 110 100 101 011, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

1 011 110 100 101 011(10) = 0000 0000 0000 0011 1001 0111 1001 1001 0110 1010 0101 1000 0110 0111 1001 0011

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


More operations of this kind:

1 011 110 100 101 010 = ? | 1 011 110 100 101 012 = ?


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

1,011,110,100,101,011 to signed binary one's complement = ? Mar 01 04:20 UTC (GMT)
3,030 to signed binary one's complement = ? Mar 01 04:19 UTC (GMT)
71 to signed binary one's complement = ? Mar 01 04:19 UTC (GMT)
-65,333 to signed binary one's complement = ? Mar 01 04:19 UTC (GMT)
4,090 to signed binary one's complement = ? Mar 01 04:19 UTC (GMT)
10,001,028 to signed binary one's complement = ? Mar 01 04:18 UTC (GMT)
110,010,176 to signed binary one's complement = ? Mar 01 04:18 UTC (GMT)
-71 to signed binary one's complement = ? Mar 01 04:18 UTC (GMT)
-10,213 to signed binary one's complement = ? Mar 01 04:17 UTC (GMT)
1,210 to signed binary one's complement = ? Mar 01 04:17 UTC (GMT)
-214 to signed binary one's complement = ? Mar 01 04:17 UTC (GMT)
17,062 to signed binary one's complement = ? Mar 01 04:17 UTC (GMT)
10,000,084 to signed binary one's complement = ? Mar 01 04:17 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