Convert 110 101 011 001 951 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 110 101 011 001 951(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
110 101 011 001 951 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;
  • 110 101 011 001 951 ÷ 2 = 55 050 505 500 975 + 1;
  • 55 050 505 500 975 ÷ 2 = 27 525 252 750 487 + 1;
  • 27 525 252 750 487 ÷ 2 = 13 762 626 375 243 + 1;
  • 13 762 626 375 243 ÷ 2 = 6 881 313 187 621 + 1;
  • 6 881 313 187 621 ÷ 2 = 3 440 656 593 810 + 1;
  • 3 440 656 593 810 ÷ 2 = 1 720 328 296 905 + 0;
  • 1 720 328 296 905 ÷ 2 = 860 164 148 452 + 1;
  • 860 164 148 452 ÷ 2 = 430 082 074 226 + 0;
  • 430 082 074 226 ÷ 2 = 215 041 037 113 + 0;
  • 215 041 037 113 ÷ 2 = 107 520 518 556 + 1;
  • 107 520 518 556 ÷ 2 = 53 760 259 278 + 0;
  • 53 760 259 278 ÷ 2 = 26 880 129 639 + 0;
  • 26 880 129 639 ÷ 2 = 13 440 064 819 + 1;
  • 13 440 064 819 ÷ 2 = 6 720 032 409 + 1;
  • 6 720 032 409 ÷ 2 = 3 360 016 204 + 1;
  • 3 360 016 204 ÷ 2 = 1 680 008 102 + 0;
  • 1 680 008 102 ÷ 2 = 840 004 051 + 0;
  • 840 004 051 ÷ 2 = 420 002 025 + 1;
  • 420 002 025 ÷ 2 = 210 001 012 + 1;
  • 210 001 012 ÷ 2 = 105 000 506 + 0;
  • 105 000 506 ÷ 2 = 52 500 253 + 0;
  • 52 500 253 ÷ 2 = 26 250 126 + 1;
  • 26 250 126 ÷ 2 = 13 125 063 + 0;
  • 13 125 063 ÷ 2 = 6 562 531 + 1;
  • 6 562 531 ÷ 2 = 3 281 265 + 1;
  • 3 281 265 ÷ 2 = 1 640 632 + 1;
  • 1 640 632 ÷ 2 = 820 316 + 0;
  • 820 316 ÷ 2 = 410 158 + 0;
  • 410 158 ÷ 2 = 205 079 + 0;
  • 205 079 ÷ 2 = 102 539 + 1;
  • 102 539 ÷ 2 = 51 269 + 1;
  • 51 269 ÷ 2 = 25 634 + 1;
  • 25 634 ÷ 2 = 12 817 + 0;
  • 12 817 ÷ 2 = 6 408 + 1;
  • 6 408 ÷ 2 = 3 204 + 0;
  • 3 204 ÷ 2 = 1 602 + 0;
  • 1 602 ÷ 2 = 801 + 0;
  • 801 ÷ 2 = 400 + 1;
  • 400 ÷ 2 = 200 + 0;
  • 200 ÷ 2 = 100 + 0;
  • 100 ÷ 2 = 50 + 0;
  • 50 ÷ 2 = 25 + 0;
  • 25 ÷ 2 = 12 + 1;
  • 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.

110 101 011 001 951(10) = 110 0100 0010 0010 1110 0011 1010 0110 0111 0010 0101 1111(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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, 47,

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 110 101 011 001 951(10) converted to signed binary in one's complement representation:

110 101 011 001 951(10) = 0000 0000 0000 0000 0110 0100 0010 0010 1110 0011 1010 0110 0111 0010 0101 1111

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