Convert 1 100 000 000 110 464 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 100 000 000 110 464(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 100 000 000 110 464 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;
  • 1 100 000 000 110 464 ÷ 2 = 550 000 000 055 232 + 0;
  • 550 000 000 055 232 ÷ 2 = 275 000 000 027 616 + 0;
  • 275 000 000 027 616 ÷ 2 = 137 500 000 013 808 + 0;
  • 137 500 000 013 808 ÷ 2 = 68 750 000 006 904 + 0;
  • 68 750 000 006 904 ÷ 2 = 34 375 000 003 452 + 0;
  • 34 375 000 003 452 ÷ 2 = 17 187 500 001 726 + 0;
  • 17 187 500 001 726 ÷ 2 = 8 593 750 000 863 + 0;
  • 8 593 750 000 863 ÷ 2 = 4 296 875 000 431 + 1;
  • 4 296 875 000 431 ÷ 2 = 2 148 437 500 215 + 1;
  • 2 148 437 500 215 ÷ 2 = 1 074 218 750 107 + 1;
  • 1 074 218 750 107 ÷ 2 = 537 109 375 053 + 1;
  • 537 109 375 053 ÷ 2 = 268 554 687 526 + 1;
  • 268 554 687 526 ÷ 2 = 134 277 343 763 + 0;
  • 134 277 343 763 ÷ 2 = 67 138 671 881 + 1;
  • 67 138 671 881 ÷ 2 = 33 569 335 940 + 1;
  • 33 569 335 940 ÷ 2 = 16 784 667 970 + 0;
  • 16 784 667 970 ÷ 2 = 8 392 333 985 + 0;
  • 8 392 333 985 ÷ 2 = 4 196 166 992 + 1;
  • 4 196 166 992 ÷ 2 = 2 098 083 496 + 0;
  • 2 098 083 496 ÷ 2 = 1 049 041 748 + 0;
  • 1 049 041 748 ÷ 2 = 524 520 874 + 0;
  • 524 520 874 ÷ 2 = 262 260 437 + 0;
  • 262 260 437 ÷ 2 = 131 130 218 + 1;
  • 131 130 218 ÷ 2 = 65 565 109 + 0;
  • 65 565 109 ÷ 2 = 32 782 554 + 1;
  • 32 782 554 ÷ 2 = 16 391 277 + 0;
  • 16 391 277 ÷ 2 = 8 195 638 + 1;
  • 8 195 638 ÷ 2 = 4 097 819 + 0;
  • 4 097 819 ÷ 2 = 2 048 909 + 1;
  • 2 048 909 ÷ 2 = 1 024 454 + 1;
  • 1 024 454 ÷ 2 = 512 227 + 0;
  • 512 227 ÷ 2 = 256 113 + 1;
  • 256 113 ÷ 2 = 128 056 + 1;
  • 128 056 ÷ 2 = 64 028 + 0;
  • 64 028 ÷ 2 = 32 014 + 0;
  • 32 014 ÷ 2 = 16 007 + 0;
  • 16 007 ÷ 2 = 8 003 + 1;
  • 8 003 ÷ 2 = 4 001 + 1;
  • 4 001 ÷ 2 = 2 000 + 1;
  • 2 000 ÷ 2 = 1 000 + 0;
  • 1 000 ÷ 2 = 500 + 0;
  • 500 ÷ 2 = 250 + 0;
  • 250 ÷ 2 = 125 + 0;
  • 125 ÷ 2 = 62 + 1;
  • 62 ÷ 2 = 31 + 0;
  • 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.

1 100 000 000 110 464(10) = 11 1110 1000 0111 0001 1011 0101 0100 0010 0110 1111 1000 0000(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 1 100 000 000 110 464(10) converted to signed binary in one's complement representation:

1 100 000 000 110 464(10) = 0000 0000 0000 0011 1110 1000 0111 0001 1011 0101 0100 0010 0110 1111 1000 0000

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