Convert -365 501 712 963 783 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number -365 501 712 963 783(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
-365 501 712 963 783 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. Start with the positive version of the number:

|-365 501 712 963 783| = 365 501 712 963 783

2. 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;
  • 365 501 712 963 783 ÷ 2 = 182 750 856 481 891 + 1;
  • 182 750 856 481 891 ÷ 2 = 91 375 428 240 945 + 1;
  • 91 375 428 240 945 ÷ 2 = 45 687 714 120 472 + 1;
  • 45 687 714 120 472 ÷ 2 = 22 843 857 060 236 + 0;
  • 22 843 857 060 236 ÷ 2 = 11 421 928 530 118 + 0;
  • 11 421 928 530 118 ÷ 2 = 5 710 964 265 059 + 0;
  • 5 710 964 265 059 ÷ 2 = 2 855 482 132 529 + 1;
  • 2 855 482 132 529 ÷ 2 = 1 427 741 066 264 + 1;
  • 1 427 741 066 264 ÷ 2 = 713 870 533 132 + 0;
  • 713 870 533 132 ÷ 2 = 356 935 266 566 + 0;
  • 356 935 266 566 ÷ 2 = 178 467 633 283 + 0;
  • 178 467 633 283 ÷ 2 = 89 233 816 641 + 1;
  • 89 233 816 641 ÷ 2 = 44 616 908 320 + 1;
  • 44 616 908 320 ÷ 2 = 22 308 454 160 + 0;
  • 22 308 454 160 ÷ 2 = 11 154 227 080 + 0;
  • 11 154 227 080 ÷ 2 = 5 577 113 540 + 0;
  • 5 577 113 540 ÷ 2 = 2 788 556 770 + 0;
  • 2 788 556 770 ÷ 2 = 1 394 278 385 + 0;
  • 1 394 278 385 ÷ 2 = 697 139 192 + 1;
  • 697 139 192 ÷ 2 = 348 569 596 + 0;
  • 348 569 596 ÷ 2 = 174 284 798 + 0;
  • 174 284 798 ÷ 2 = 87 142 399 + 0;
  • 87 142 399 ÷ 2 = 43 571 199 + 1;
  • 43 571 199 ÷ 2 = 21 785 599 + 1;
  • 21 785 599 ÷ 2 = 10 892 799 + 1;
  • 10 892 799 ÷ 2 = 5 446 399 + 1;
  • 5 446 399 ÷ 2 = 2 723 199 + 1;
  • 2 723 199 ÷ 2 = 1 361 599 + 1;
  • 1 361 599 ÷ 2 = 680 799 + 1;
  • 680 799 ÷ 2 = 340 399 + 1;
  • 340 399 ÷ 2 = 170 199 + 1;
  • 170 199 ÷ 2 = 85 099 + 1;
  • 85 099 ÷ 2 = 42 549 + 1;
  • 42 549 ÷ 2 = 21 274 + 1;
  • 21 274 ÷ 2 = 10 637 + 0;
  • 10 637 ÷ 2 = 5 318 + 1;
  • 5 318 ÷ 2 = 2 659 + 0;
  • 2 659 ÷ 2 = 1 329 + 1;
  • 1 329 ÷ 2 = 664 + 1;
  • 664 ÷ 2 = 332 + 0;
  • 332 ÷ 2 = 166 + 0;
  • 166 ÷ 2 = 83 + 0;
  • 83 ÷ 2 = 41 + 1;
  • 41 ÷ 2 = 20 + 1;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

365 501 712 963 783(10) = 1 0100 1100 0110 1011 1111 1111 1100 0100 0001 1000 1100 0111(2)

4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 49.

  • 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, 49,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


5. 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.


365 501 712 963 783(10) = 0000 0000 0000 0001 0100 1100 0110 1011 1111 1111 1100 0100 0001 1000 1100 0111

6. Get the negative integer number representation:

  • To write the negative integer number on 64 bits (8 Bytes), as a signed binary in one's complement representation,

  • ... Reverse all the bits from 0 to 1 and from 1 to 0 (flip the digits).


-365 501 712 963 783(10) = !(0000 0000 0000 0001 0100 1100 0110 1011 1111 1111 1100 0100 0001 1000 1100 0111)


Decimal Number -365 501 712 963 783(10) converted to signed binary in one's complement representation:

-365 501 712 963 783(10) = 1111 1111 1111 1110 1011 0011 1001 0100 0000 0000 0011 1011 1110 0111 0011 1000

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