Convert Decimal 1 000 000 000 000 000 066 to Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 000 000 000 000 000 066(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 000 000 000 000 000 066 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;
  • 1 000 000 000 000 000 066 ÷ 2 = 500 000 000 000 000 033 + 0;
  • 500 000 000 000 000 033 ÷ 2 = 250 000 000 000 000 016 + 1;
  • 250 000 000 000 000 016 ÷ 2 = 125 000 000 000 000 008 + 0;
  • 125 000 000 000 000 008 ÷ 2 = 62 500 000 000 000 004 + 0;
  • 62 500 000 000 000 004 ÷ 2 = 31 250 000 000 000 002 + 0;
  • 31 250 000 000 000 002 ÷ 2 = 15 625 000 000 000 001 + 0;
  • 15 625 000 000 000 001 ÷ 2 = 7 812 500 000 000 000 + 1;
  • 7 812 500 000 000 000 ÷ 2 = 3 906 250 000 000 000 + 0;
  • 3 906 250 000 000 000 ÷ 2 = 1 953 125 000 000 000 + 0;
  • 1 953 125 000 000 000 ÷ 2 = 976 562 500 000 000 + 0;
  • 976 562 500 000 000 ÷ 2 = 488 281 250 000 000 + 0;
  • 488 281 250 000 000 ÷ 2 = 244 140 625 000 000 + 0;
  • 244 140 625 000 000 ÷ 2 = 122 070 312 500 000 + 0;
  • 122 070 312 500 000 ÷ 2 = 61 035 156 250 000 + 0;
  • 61 035 156 250 000 ÷ 2 = 30 517 578 125 000 + 0;
  • 30 517 578 125 000 ÷ 2 = 15 258 789 062 500 + 0;
  • 15 258 789 062 500 ÷ 2 = 7 629 394 531 250 + 0;
  • 7 629 394 531 250 ÷ 2 = 3 814 697 265 625 + 0;
  • 3 814 697 265 625 ÷ 2 = 1 907 348 632 812 + 1;
  • 1 907 348 632 812 ÷ 2 = 953 674 316 406 + 0;
  • 953 674 316 406 ÷ 2 = 476 837 158 203 + 0;
  • 476 837 158 203 ÷ 2 = 238 418 579 101 + 1;
  • 238 418 579 101 ÷ 2 = 119 209 289 550 + 1;
  • 119 209 289 550 ÷ 2 = 59 604 644 775 + 0;
  • 59 604 644 775 ÷ 2 = 29 802 322 387 + 1;
  • 29 802 322 387 ÷ 2 = 14 901 161 193 + 1;
  • 14 901 161 193 ÷ 2 = 7 450 580 596 + 1;
  • 7 450 580 596 ÷ 2 = 3 725 290 298 + 0;
  • 3 725 290 298 ÷ 2 = 1 862 645 149 + 0;
  • 1 862 645 149 ÷ 2 = 931 322 574 + 1;
  • 931 322 574 ÷ 2 = 465 661 287 + 0;
  • 465 661 287 ÷ 2 = 232 830 643 + 1;
  • 232 830 643 ÷ 2 = 116 415 321 + 1;
  • 116 415 321 ÷ 2 = 58 207 660 + 1;
  • 58 207 660 ÷ 2 = 29 103 830 + 0;
  • 29 103 830 ÷ 2 = 14 551 915 + 0;
  • 14 551 915 ÷ 2 = 7 275 957 + 1;
  • 7 275 957 ÷ 2 = 3 637 978 + 1;
  • 3 637 978 ÷ 2 = 1 818 989 + 0;
  • 1 818 989 ÷ 2 = 909 494 + 1;
  • 909 494 ÷ 2 = 454 747 + 0;
  • 454 747 ÷ 2 = 227 373 + 1;
  • 227 373 ÷ 2 = 113 686 + 1;
  • 113 686 ÷ 2 = 56 843 + 0;
  • 56 843 ÷ 2 = 28 421 + 1;
  • 28 421 ÷ 2 = 14 210 + 1;
  • 14 210 ÷ 2 = 7 105 + 0;
  • 7 105 ÷ 2 = 3 552 + 1;
  • 3 552 ÷ 2 = 1 776 + 0;
  • 1 776 ÷ 2 = 888 + 0;
  • 888 ÷ 2 = 444 + 0;
  • 444 ÷ 2 = 222 + 0;
  • 222 ÷ 2 = 111 + 0;
  • 111 ÷ 2 = 55 + 1;
  • 55 ÷ 2 = 27 + 1;
  • 27 ÷ 2 = 13 + 1;
  • 13 ÷ 2 = 6 + 1;
  • 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.

1 000 000 000 000 000 066(10) = 1101 1110 0000 1011 0110 1011 0011 1010 0111 0110 0100 0000 0000 0100 0010(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 60.

  • 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, 60,

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 1 000 000 000 000 000 066(10) converted to signed binary in one's complement representation:

1 000 000 000 000 000 066(10) = 0000 1101 1110 0000 1011 0110 1011 0011 1010 0111 0110 0100 0000 0000 0100 0010

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