Convert 1 000 000 100 009 984 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

1 000 000 100 009 984(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;
  • 1 000 000 100 009 984 ÷ 2 = 500 000 050 004 992 + 0;
  • 500 000 050 004 992 ÷ 2 = 250 000 025 002 496 + 0;
  • 250 000 025 002 496 ÷ 2 = 125 000 012 501 248 + 0;
  • 125 000 012 501 248 ÷ 2 = 62 500 006 250 624 + 0;
  • 62 500 006 250 624 ÷ 2 = 31 250 003 125 312 + 0;
  • 31 250 003 125 312 ÷ 2 = 15 625 001 562 656 + 0;
  • 15 625 001 562 656 ÷ 2 = 7 812 500 781 328 + 0;
  • 7 812 500 781 328 ÷ 2 = 3 906 250 390 664 + 0;
  • 3 906 250 390 664 ÷ 2 = 1 953 125 195 332 + 0;
  • 1 953 125 195 332 ÷ 2 = 976 562 597 666 + 0;
  • 976 562 597 666 ÷ 2 = 488 281 298 833 + 0;
  • 488 281 298 833 ÷ 2 = 244 140 649 416 + 1;
  • 244 140 649 416 ÷ 2 = 122 070 324 708 + 0;
  • 122 070 324 708 ÷ 2 = 61 035 162 354 + 0;
  • 61 035 162 354 ÷ 2 = 30 517 581 177 + 0;
  • 30 517 581 177 ÷ 2 = 15 258 790 588 + 1;
  • 15 258 790 588 ÷ 2 = 7 629 395 294 + 0;
  • 7 629 395 294 ÷ 2 = 3 814 697 647 + 0;
  • 3 814 697 647 ÷ 2 = 1 907 348 823 + 1;
  • 1 907 348 823 ÷ 2 = 953 674 411 + 1;
  • 953 674 411 ÷ 2 = 476 837 205 + 1;
  • 476 837 205 ÷ 2 = 238 418 602 + 1;
  • 238 418 602 ÷ 2 = 119 209 301 + 0;
  • 119 209 301 ÷ 2 = 59 604 650 + 1;
  • 59 604 650 ÷ 2 = 29 802 325 + 0;
  • 29 802 325 ÷ 2 = 14 901 162 + 1;
  • 14 901 162 ÷ 2 = 7 450 581 + 0;
  • 7 450 581 ÷ 2 = 3 725 290 + 1;
  • 3 725 290 ÷ 2 = 1 862 645 + 0;
  • 1 862 645 ÷ 2 = 931 322 + 1;
  • 931 322 ÷ 2 = 465 661 + 0;
  • 465 661 ÷ 2 = 232 830 + 1;
  • 232 830 ÷ 2 = 116 415 + 0;
  • 116 415 ÷ 2 = 58 207 + 1;
  • 58 207 ÷ 2 = 29 103 + 1;
  • 29 103 ÷ 2 = 14 551 + 1;
  • 14 551 ÷ 2 = 7 275 + 1;
  • 7 275 ÷ 2 = 3 637 + 1;
  • 3 637 ÷ 2 = 1 818 + 1;
  • 1 818 ÷ 2 = 909 + 0;
  • 909 ÷ 2 = 454 + 1;
  • 454 ÷ 2 = 227 + 0;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 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.

1 000 000 100 009 984(10) = 11 1000 1101 0111 1110 1010 1010 1011 1100 1000 1000 0000 0000(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:

1 000 000 100 009 984(10) = 0000 0000 0000 0011 1000 1101 0111 1110 1010 1010 1011 1100 1000 1000 0000 0000


Number 1 000 000 100 009 984, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

1 000 000 100 009 984(10) = 0000 0000 0000 0011 1000 1101 0111 1110 1010 1010 1011 1100 1000 1000 0000 0000

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


More operations of this kind:

1 000 000 100 009 983 = ? | 1 000 000 100 009 985 = ?


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

1,000,000,100,009,984 to signed binary one's complement = ? Jul 24 12:19 UTC (GMT)
-6,532 to signed binary one's complement = ? Jul 24 12:19 UTC (GMT)
852 to signed binary one's complement = ? Jul 24 12:18 UTC (GMT)
51,971 to signed binary one's complement = ? Jul 24 12:18 UTC (GMT)
100,000,110,121 to signed binary one's complement = ? Jul 24 12:18 UTC (GMT)
111,099 to signed binary one's complement = ? Jul 24 12:18 UTC (GMT)
571,275 to signed binary one's complement = ? Jul 24 12:18 UTC (GMT)
1,000,011 to signed binary one's complement = ? Jul 24 12:17 UTC (GMT)
33,554,450 to signed binary one's complement = ? Jul 24 12:17 UTC (GMT)
-37 to signed binary one's complement = ? Jul 24 12:16 UTC (GMT)
-372 to signed binary one's complement = ? Jul 24 12:16 UTC (GMT)
4,538 to signed binary one's complement = ? Jul 24 12:16 UTC (GMT)
11,010,934 to signed binary one's complement = ? Jul 24 12:16 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