Convert 1 100 010 101 933 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 100 010 101 933(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 100 010 101 933 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;
  • 1 100 010 101 933 ÷ 2 = 550 005 050 966 + 1;
  • 550 005 050 966 ÷ 2 = 275 002 525 483 + 0;
  • 275 002 525 483 ÷ 2 = 137 501 262 741 + 1;
  • 137 501 262 741 ÷ 2 = 68 750 631 370 + 1;
  • 68 750 631 370 ÷ 2 = 34 375 315 685 + 0;
  • 34 375 315 685 ÷ 2 = 17 187 657 842 + 1;
  • 17 187 657 842 ÷ 2 = 8 593 828 921 + 0;
  • 8 593 828 921 ÷ 2 = 4 296 914 460 + 1;
  • 4 296 914 460 ÷ 2 = 2 148 457 230 + 0;
  • 2 148 457 230 ÷ 2 = 1 074 228 615 + 0;
  • 1 074 228 615 ÷ 2 = 537 114 307 + 1;
  • 537 114 307 ÷ 2 = 268 557 153 + 1;
  • 268 557 153 ÷ 2 = 134 278 576 + 1;
  • 134 278 576 ÷ 2 = 67 139 288 + 0;
  • 67 139 288 ÷ 2 = 33 569 644 + 0;
  • 33 569 644 ÷ 2 = 16 784 822 + 0;
  • 16 784 822 ÷ 2 = 8 392 411 + 0;
  • 8 392 411 ÷ 2 = 4 196 205 + 1;
  • 4 196 205 ÷ 2 = 2 098 102 + 1;
  • 2 098 102 ÷ 2 = 1 049 051 + 0;
  • 1 049 051 ÷ 2 = 524 525 + 1;
  • 524 525 ÷ 2 = 262 262 + 1;
  • 262 262 ÷ 2 = 131 131 + 0;
  • 131 131 ÷ 2 = 65 565 + 1;
  • 65 565 ÷ 2 = 32 782 + 1;
  • 32 782 ÷ 2 = 16 391 + 0;
  • 16 391 ÷ 2 = 8 195 + 1;
  • 8 195 ÷ 2 = 4 097 + 1;
  • 4 097 ÷ 2 = 2 048 + 1;
  • 2 048 ÷ 2 = 1 024 + 0;
  • 1 024 ÷ 2 = 512 + 0;
  • 512 ÷ 2 = 256 + 0;
  • 256 ÷ 2 = 128 + 0;
  • 128 ÷ 2 = 64 + 0;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 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.

1 100 010 101 933(10) = 1 0000 0000 0001 1101 1011 0110 0001 1100 1010 1101(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 41.

  • 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, 41,

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 1 100 010 101 933(10) converted to signed binary in one's complement representation:

1 100 010 101 933(10) = 0000 0000 0000 0000 0000 0001 0000 0000 0001 1101 1011 0110 0001 1100 1010 1101

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