Convert 1 111 110 101 100 140 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 111 110 101 100 140(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 111 110 101 100 140 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;
  • 1 111 110 101 100 140 ÷ 2 = 555 555 050 550 070 + 0;
  • 555 555 050 550 070 ÷ 2 = 277 777 525 275 035 + 0;
  • 277 777 525 275 035 ÷ 2 = 138 888 762 637 517 + 1;
  • 138 888 762 637 517 ÷ 2 = 69 444 381 318 758 + 1;
  • 69 444 381 318 758 ÷ 2 = 34 722 190 659 379 + 0;
  • 34 722 190 659 379 ÷ 2 = 17 361 095 329 689 + 1;
  • 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.

1 111 110 101 100 140(10) = 11 1111 0010 1000 1100 0111 1010 1110 0001 1110 0110 0110 1100(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 1 111 110 101 100 140(10) converted to signed binary in one's complement representation:

1 111 110 101 100 140(10) = 0000 0000 0000 0011 1111 0010 1000 1100 0111 1010 1110 0001 1110 0110 0110 1100

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