Convert 110 111 101 011 110 361 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 110 111 101 011 110 361(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
110 111 101 011 110 361 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;
  • 110 111 101 011 110 361 ÷ 2 = 55 055 550 505 555 180 + 1;
  • 55 055 550 505 555 180 ÷ 2 = 27 527 775 252 777 590 + 0;
  • 27 527 775 252 777 590 ÷ 2 = 13 763 887 626 388 795 + 0;
  • 13 763 887 626 388 795 ÷ 2 = 6 881 943 813 194 397 + 1;
  • 6 881 943 813 194 397 ÷ 2 = 3 440 971 906 597 198 + 1;
  • 3 440 971 906 597 198 ÷ 2 = 1 720 485 953 298 599 + 0;
  • 1 720 485 953 298 599 ÷ 2 = 860 242 976 649 299 + 1;
  • 860 242 976 649 299 ÷ 2 = 430 121 488 324 649 + 1;
  • 430 121 488 324 649 ÷ 2 = 215 060 744 162 324 + 1;
  • 215 060 744 162 324 ÷ 2 = 107 530 372 081 162 + 0;
  • 107 530 372 081 162 ÷ 2 = 53 765 186 040 581 + 0;
  • 53 765 186 040 581 ÷ 2 = 26 882 593 020 290 + 1;
  • 26 882 593 020 290 ÷ 2 = 13 441 296 510 145 + 0;
  • 13 441 296 510 145 ÷ 2 = 6 720 648 255 072 + 1;
  • 6 720 648 255 072 ÷ 2 = 3 360 324 127 536 + 0;
  • 3 360 324 127 536 ÷ 2 = 1 680 162 063 768 + 0;
  • 1 680 162 063 768 ÷ 2 = 840 081 031 884 + 0;
  • 840 081 031 884 ÷ 2 = 420 040 515 942 + 0;
  • 420 040 515 942 ÷ 2 = 210 020 257 971 + 0;
  • 210 020 257 971 ÷ 2 = 105 010 128 985 + 1;
  • 105 010 128 985 ÷ 2 = 52 505 064 492 + 1;
  • 52 505 064 492 ÷ 2 = 26 252 532 246 + 0;
  • 26 252 532 246 ÷ 2 = 13 126 266 123 + 0;
  • 13 126 266 123 ÷ 2 = 6 563 133 061 + 1;
  • 6 563 133 061 ÷ 2 = 3 281 566 530 + 1;
  • 3 281 566 530 ÷ 2 = 1 640 783 265 + 0;
  • 1 640 783 265 ÷ 2 = 820 391 632 + 1;
  • 820 391 632 ÷ 2 = 410 195 816 + 0;
  • 410 195 816 ÷ 2 = 205 097 908 + 0;
  • 205 097 908 ÷ 2 = 102 548 954 + 0;
  • 102 548 954 ÷ 2 = 51 274 477 + 0;
  • 51 274 477 ÷ 2 = 25 637 238 + 1;
  • 25 637 238 ÷ 2 = 12 818 619 + 0;
  • 12 818 619 ÷ 2 = 6 409 309 + 1;
  • 6 409 309 ÷ 2 = 3 204 654 + 1;
  • 3 204 654 ÷ 2 = 1 602 327 + 0;
  • 1 602 327 ÷ 2 = 801 163 + 1;
  • 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.

110 111 101 011 110 361(10) = 1 1000 0111 0011 0001 0111 0110 1000 0101 1001 1000 0010 1001 1101 1001(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 110 111 101 011 110 361(10) converted to signed binary in one's complement representation:

110 111 101 011 110 361(10) = 0000 0001 1000 0111 0011 0001 0111 0110 1000 0101 1001 1000 0010 1001 1101 1001

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