Convert 1 111 110 101 100 125 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

1 111 110 101 100 125(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;
  • 1 111 110 101 100 125 ÷ 2 = 555 555 050 550 062 + 1;
  • 555 555 050 550 062 ÷ 2 = 277 777 525 275 031 + 0;
  • 277 777 525 275 031 ÷ 2 = 138 888 762 637 515 + 1;
  • 138 888 762 637 515 ÷ 2 = 69 444 381 318 757 + 1;
  • 69 444 381 318 757 ÷ 2 = 34 722 190 659 378 + 1;
  • 34 722 190 659 378 ÷ 2 = 17 361 095 329 689 + 0;
  • 17 361 095 329 689 ÷ 2 = 8 680 547 664 844 + 1;
  • 8 680 547 664 844 ÷ 2 = 4 340 273 832 422 + 0;
  • 4 340 273 832 422 ÷ 2 = 2 170 136 916 211 + 0;
  • 2 170 136 916 211 ÷ 2 = 1 085 068 458 105 + 1;
  • 1 085 068 458 105 ÷ 2 = 542 534 229 052 + 1;
  • 542 534 229 052 ÷ 2 = 271 267 114 526 + 0;
  • 271 267 114 526 ÷ 2 = 135 633 557 263 + 0;
  • 135 633 557 263 ÷ 2 = 67 816 778 631 + 1;
  • 67 816 778 631 ÷ 2 = 33 908 389 315 + 1;
  • 33 908 389 315 ÷ 2 = 16 954 194 657 + 1;
  • 16 954 194 657 ÷ 2 = 8 477 097 328 + 1;
  • 8 477 097 328 ÷ 2 = 4 238 548 664 + 0;
  • 4 238 548 664 ÷ 2 = 2 119 274 332 + 0;
  • 2 119 274 332 ÷ 2 = 1 059 637 166 + 0;
  • 1 059 637 166 ÷ 2 = 529 818 583 + 0;
  • 529 818 583 ÷ 2 = 264 909 291 + 1;
  • 264 909 291 ÷ 2 = 132 454 645 + 1;
  • 132 454 645 ÷ 2 = 66 227 322 + 1;
  • 66 227 322 ÷ 2 = 33 113 661 + 0;
  • 33 113 661 ÷ 2 = 16 556 830 + 1;
  • 16 556 830 ÷ 2 = 8 278 415 + 0;
  • 8 278 415 ÷ 2 = 4 139 207 + 1;
  • 4 139 207 ÷ 2 = 2 069 603 + 1;
  • 2 069 603 ÷ 2 = 1 034 801 + 1;
  • 1 034 801 ÷ 2 = 517 400 + 1;
  • 517 400 ÷ 2 = 258 700 + 0;
  • 258 700 ÷ 2 = 129 350 + 0;
  • 129 350 ÷ 2 = 64 675 + 0;
  • 64 675 ÷ 2 = 32 337 + 1;
  • 32 337 ÷ 2 = 16 168 + 1;
  • 16 168 ÷ 2 = 8 084 + 0;
  • 8 084 ÷ 2 = 4 042 + 0;
  • 4 042 ÷ 2 = 2 021 + 0;
  • 2 021 ÷ 2 = 1 010 + 1;
  • 1 010 ÷ 2 = 505 + 0;
  • 505 ÷ 2 = 252 + 1;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.

1 111 110 101 100 125(10) = 11 1111 0010 1000 1100 0111 1010 1110 0001 1110 0110 0101 1101(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:

1 111 110 101 100 125(10) = 0000 0000 0000 0011 1111 0010 1000 1100 0111 1010 1110 0001 1110 0110 0101 1101


Number 1 111 110 101 100 125, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

1 111 110 101 100 125(10) = 0000 0000 0000 0011 1111 0010 1000 1100 0111 1010 1110 0001 1110 0110 0101 1101

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


More operations of this kind:

1 111 110 101 100 124 = ? | 1 111 110 101 100 126 = ?


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

1,111,110,101,100,125 to signed binary one's complement = ? Jul 24 10:00 UTC (GMT)
11,011,048 to signed binary one's complement = ? Jul 24 10:00 UTC (GMT)
-45 to signed binary one's complement = ? Jul 24 10:00 UTC (GMT)
-321 to signed binary one's complement = ? Jul 24 10:00 UTC (GMT)
-10,302 to signed binary one's complement = ? Jul 24 09:59 UTC (GMT)
-1,010,026 to signed binary one's complement = ? Jul 24 09:59 UTC (GMT)
19,127,308 to signed binary one's complement = ? Jul 24 09:59 UTC (GMT)
2,260 to signed binary one's complement = ? Jul 24 09:58 UTC (GMT)
10,010,095 to signed binary one's complement = ? Jul 24 09:58 UTC (GMT)
-622 to signed binary one's complement = ? Jul 24 09:58 UTC (GMT)
1,684,948,271 to signed binary one's complement = ? Jul 24 09:58 UTC (GMT)
258 to signed binary one's complement = ? Jul 24 09:57 UTC (GMT)
65,203 to signed binary one's complement = ? Jul 24 09:56 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