Convert 110 111 010 110 111 334 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 110 111 010 110 111 334(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
110 111 010 110 111 334 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;
  • 110 111 010 110 111 334 ÷ 2 = 55 055 505 055 055 667 + 0;
  • 55 055 505 055 055 667 ÷ 2 = 27 527 752 527 527 833 + 1;
  • 27 527 752 527 527 833 ÷ 2 = 13 763 876 263 763 916 + 1;
  • 13 763 876 263 763 916 ÷ 2 = 6 881 938 131 881 958 + 0;
  • 6 881 938 131 881 958 ÷ 2 = 3 440 969 065 940 979 + 0;
  • 3 440 969 065 940 979 ÷ 2 = 1 720 484 532 970 489 + 1;
  • 1 720 484 532 970 489 ÷ 2 = 860 242 266 485 244 + 1;
  • 860 242 266 485 244 ÷ 2 = 430 121 133 242 622 + 0;
  • 430 121 133 242 622 ÷ 2 = 215 060 566 621 311 + 0;
  • 215 060 566 621 311 ÷ 2 = 107 530 283 310 655 + 1;
  • 107 530 283 310 655 ÷ 2 = 53 765 141 655 327 + 1;
  • 53 765 141 655 327 ÷ 2 = 26 882 570 827 663 + 1;
  • 26 882 570 827 663 ÷ 2 = 13 441 285 413 831 + 1;
  • 13 441 285 413 831 ÷ 2 = 6 720 642 706 915 + 1;
  • 6 720 642 706 915 ÷ 2 = 3 360 321 353 457 + 1;
  • 3 360 321 353 457 ÷ 2 = 1 680 160 676 728 + 1;
  • 1 680 160 676 728 ÷ 2 = 840 080 338 364 + 0;
  • 840 080 338 364 ÷ 2 = 420 040 169 182 + 0;
  • 420 040 169 182 ÷ 2 = 210 020 084 591 + 0;
  • 210 020 084 591 ÷ 2 = 105 010 042 295 + 1;
  • 105 010 042 295 ÷ 2 = 52 505 021 147 + 1;
  • 52 505 021 147 ÷ 2 = 26 252 510 573 + 1;
  • 26 252 510 573 ÷ 2 = 13 126 255 286 + 1;
  • 13 126 255 286 ÷ 2 = 6 563 127 643 + 0;
  • 6 563 127 643 ÷ 2 = 3 281 563 821 + 1;
  • 3 281 563 821 ÷ 2 = 1 640 781 910 + 1;
  • 1 640 781 910 ÷ 2 = 820 390 955 + 0;
  • 820 390 955 ÷ 2 = 410 195 477 + 1;
  • 410 195 477 ÷ 2 = 205 097 738 + 1;
  • 205 097 738 ÷ 2 = 102 548 869 + 0;
  • 102 548 869 ÷ 2 = 51 274 434 + 1;
  • 51 274 434 ÷ 2 = 25 637 217 + 0;
  • 25 637 217 ÷ 2 = 12 818 608 + 1;
  • 12 818 608 ÷ 2 = 6 409 304 + 0;
  • 6 409 304 ÷ 2 = 3 204 652 + 0;
  • 3 204 652 ÷ 2 = 1 602 326 + 0;
  • 1 602 326 ÷ 2 = 801 163 + 0;
  • 801 163 ÷ 2 = 400 581 + 1;
  • 400 581 ÷ 2 = 200 290 + 1;
  • 200 290 ÷ 2 = 100 145 + 0;
  • 100 145 ÷ 2 = 50 072 + 1;
  • 50 072 ÷ 2 = 25 036 + 0;
  • 25 036 ÷ 2 = 12 518 + 0;
  • 12 518 ÷ 2 = 6 259 + 0;
  • 6 259 ÷ 2 = 3 129 + 1;
  • 3 129 ÷ 2 = 1 564 + 1;
  • 1 564 ÷ 2 = 782 + 0;
  • 782 ÷ 2 = 391 + 0;
  • 391 ÷ 2 = 195 + 1;
  • 195 ÷ 2 = 97 + 1;
  • 97 ÷ 2 = 48 + 1;
  • 48 ÷ 2 = 24 + 0;
  • 24 ÷ 2 = 12 + 0;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 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.

110 111 010 110 111 334(10) = 1 1000 0111 0011 0001 0110 0001 0101 1011 0111 1000 1111 1110 0110 0110(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 57.

  • 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, 57,

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 110 111 010 110 111 334(10) converted to signed binary in one's complement representation:

110 111 010 110 111 334(10) = 0000 0001 1000 0111 0011 0001 0110 0001 0101 1011 0111 1000 1111 1110 0110 0110

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