Convert 1 110 101 010 010 994 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 110 101 010 010 994(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 110 101 010 010 994 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 110 101 010 010 994 ÷ 2 = 555 050 505 005 497 + 0;
  • 555 050 505 005 497 ÷ 2 = 277 525 252 502 748 + 1;
  • 277 525 252 502 748 ÷ 2 = 138 762 626 251 374 + 0;
  • 138 762 626 251 374 ÷ 2 = 69 381 313 125 687 + 0;
  • 69 381 313 125 687 ÷ 2 = 34 690 656 562 843 + 1;
  • 34 690 656 562 843 ÷ 2 = 17 345 328 281 421 + 1;
  • 17 345 328 281 421 ÷ 2 = 8 672 664 140 710 + 1;
  • 8 672 664 140 710 ÷ 2 = 4 336 332 070 355 + 0;
  • 4 336 332 070 355 ÷ 2 = 2 168 166 035 177 + 1;
  • 2 168 166 035 177 ÷ 2 = 1 084 083 017 588 + 1;
  • 1 084 083 017 588 ÷ 2 = 542 041 508 794 + 0;
  • 542 041 508 794 ÷ 2 = 271 020 754 397 + 0;
  • 271 020 754 397 ÷ 2 = 135 510 377 198 + 1;
  • 135 510 377 198 ÷ 2 = 67 755 188 599 + 0;
  • 67 755 188 599 ÷ 2 = 33 877 594 299 + 1;
  • 33 877 594 299 ÷ 2 = 16 938 797 149 + 1;
  • 16 938 797 149 ÷ 2 = 8 469 398 574 + 1;
  • 8 469 398 574 ÷ 2 = 4 234 699 287 + 0;
  • 4 234 699 287 ÷ 2 = 2 117 349 643 + 1;
  • 2 117 349 643 ÷ 2 = 1 058 674 821 + 1;
  • 1 058 674 821 ÷ 2 = 529 337 410 + 1;
  • 529 337 410 ÷ 2 = 264 668 705 + 0;
  • 264 668 705 ÷ 2 = 132 334 352 + 1;
  • 132 334 352 ÷ 2 = 66 167 176 + 0;
  • 66 167 176 ÷ 2 = 33 083 588 + 0;
  • 33 083 588 ÷ 2 = 16 541 794 + 0;
  • 16 541 794 ÷ 2 = 8 270 897 + 0;
  • 8 270 897 ÷ 2 = 4 135 448 + 1;
  • 4 135 448 ÷ 2 = 2 067 724 + 0;
  • 2 067 724 ÷ 2 = 1 033 862 + 0;
  • 1 033 862 ÷ 2 = 516 931 + 0;
  • 516 931 ÷ 2 = 258 465 + 1;
  • 258 465 ÷ 2 = 129 232 + 1;
  • 129 232 ÷ 2 = 64 616 + 0;
  • 64 616 ÷ 2 = 32 308 + 0;
  • 32 308 ÷ 2 = 16 154 + 0;
  • 16 154 ÷ 2 = 8 077 + 0;
  • 8 077 ÷ 2 = 4 038 + 1;
  • 4 038 ÷ 2 = 2 019 + 0;
  • 2 019 ÷ 2 = 1 009 + 1;
  • 1 009 ÷ 2 = 504 + 1;
  • 504 ÷ 2 = 252 + 0;
  • 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.

1 110 101 010 010 994(10) = 11 1111 0001 1010 0001 1000 1000 0101 1101 1101 0011 0111 0010(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; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 50,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the 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.


Decimal Number 1 110 101 010 010 994(10) converted to signed binary in one's complement representation:

1 110 101 010 010 994(10) = 0000 0000 0000 0011 1111 0001 1010 0001 1000 1000 0101 1101 1101 0011 0111 0010

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

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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