Convert 10 111 011 100 751 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 10 111 011 100 751(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
10 111 011 100 751 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;
  • 10 111 011 100 751 ÷ 2 = 5 055 505 550 375 + 1;
  • 5 055 505 550 375 ÷ 2 = 2 527 752 775 187 + 1;
  • 2 527 752 775 187 ÷ 2 = 1 263 876 387 593 + 1;
  • 1 263 876 387 593 ÷ 2 = 631 938 193 796 + 1;
  • 631 938 193 796 ÷ 2 = 315 969 096 898 + 0;
  • 315 969 096 898 ÷ 2 = 157 984 548 449 + 0;
  • 157 984 548 449 ÷ 2 = 78 992 274 224 + 1;
  • 78 992 274 224 ÷ 2 = 39 496 137 112 + 0;
  • 39 496 137 112 ÷ 2 = 19 748 068 556 + 0;
  • 19 748 068 556 ÷ 2 = 9 874 034 278 + 0;
  • 9 874 034 278 ÷ 2 = 4 937 017 139 + 0;
  • 4 937 017 139 ÷ 2 = 2 468 508 569 + 1;
  • 2 468 508 569 ÷ 2 = 1 234 254 284 + 1;
  • 1 234 254 284 ÷ 2 = 617 127 142 + 0;
  • 617 127 142 ÷ 2 = 308 563 571 + 0;
  • 308 563 571 ÷ 2 = 154 281 785 + 1;
  • 154 281 785 ÷ 2 = 77 140 892 + 1;
  • 77 140 892 ÷ 2 = 38 570 446 + 0;
  • 38 570 446 ÷ 2 = 19 285 223 + 0;
  • 19 285 223 ÷ 2 = 9 642 611 + 1;
  • 9 642 611 ÷ 2 = 4 821 305 + 1;
  • 4 821 305 ÷ 2 = 2 410 652 + 1;
  • 2 410 652 ÷ 2 = 1 205 326 + 0;
  • 1 205 326 ÷ 2 = 602 663 + 0;
  • 602 663 ÷ 2 = 301 331 + 1;
  • 301 331 ÷ 2 = 150 665 + 1;
  • 150 665 ÷ 2 = 75 332 + 1;
  • 75 332 ÷ 2 = 37 666 + 0;
  • 37 666 ÷ 2 = 18 833 + 0;
  • 18 833 ÷ 2 = 9 416 + 1;
  • 9 416 ÷ 2 = 4 708 + 0;
  • 4 708 ÷ 2 = 2 354 + 0;
  • 2 354 ÷ 2 = 1 177 + 0;
  • 1 177 ÷ 2 = 588 + 1;
  • 588 ÷ 2 = 294 + 0;
  • 294 ÷ 2 = 147 + 0;
  • 147 ÷ 2 = 73 + 1;
  • 73 ÷ 2 = 36 + 1;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 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.

10 111 011 100 751(10) = 1001 0011 0010 0010 0111 0011 1001 1001 1000 0100 1111(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 44.

  • 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, 44,

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 10 111 011 100 751(10) converted to signed binary in one's complement representation:

10 111 011 100 751(10) = 0000 0000 0000 0000 0000 1001 0011 0010 0010 0111 0011 1001 1001 1000 0100 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