Two's Complement: Integer ↗ Binary: 486 663 237 694 Convert the Integer Number to a Signed Binary in Two's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 486 663 237 694(10) converted and written as a signed binary in two's complement representation (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 486 663 237 694 ÷ 2 = 243 331 618 847 + 0;
  • 243 331 618 847 ÷ 2 = 121 665 809 423 + 1;
  • 121 665 809 423 ÷ 2 = 60 832 904 711 + 1;
  • 60 832 904 711 ÷ 2 = 30 416 452 355 + 1;
  • 30 416 452 355 ÷ 2 = 15 208 226 177 + 1;
  • 15 208 226 177 ÷ 2 = 7 604 113 088 + 1;
  • 7 604 113 088 ÷ 2 = 3 802 056 544 + 0;
  • 3 802 056 544 ÷ 2 = 1 901 028 272 + 0;
  • 1 901 028 272 ÷ 2 = 950 514 136 + 0;
  • 950 514 136 ÷ 2 = 475 257 068 + 0;
  • 475 257 068 ÷ 2 = 237 628 534 + 0;
  • 237 628 534 ÷ 2 = 118 814 267 + 0;
  • 118 814 267 ÷ 2 = 59 407 133 + 1;
  • 59 407 133 ÷ 2 = 29 703 566 + 1;
  • 29 703 566 ÷ 2 = 14 851 783 + 0;
  • 14 851 783 ÷ 2 = 7 425 891 + 1;
  • 7 425 891 ÷ 2 = 3 712 945 + 1;
  • 3 712 945 ÷ 2 = 1 856 472 + 1;
  • 1 856 472 ÷ 2 = 928 236 + 0;
  • 928 236 ÷ 2 = 464 118 + 0;
  • 464 118 ÷ 2 = 232 059 + 0;
  • 232 059 ÷ 2 = 116 029 + 1;
  • 116 029 ÷ 2 = 58 014 + 1;
  • 58 014 ÷ 2 = 29 007 + 0;
  • 29 007 ÷ 2 = 14 503 + 1;
  • 14 503 ÷ 2 = 7 251 + 1;
  • 7 251 ÷ 2 = 3 625 + 1;
  • 3 625 ÷ 2 = 1 812 + 1;
  • 1 812 ÷ 2 = 906 + 0;
  • 906 ÷ 2 = 453 + 0;
  • 453 ÷ 2 = 226 + 1;
  • 226 ÷ 2 = 113 + 0;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 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.


486 663 237 694(10) = 111 0001 0100 1111 0110 0011 1011 0000 0011 1110(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 39.


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, 39,

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.


Number 486 663 237 694(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:

486 663 237 694(10) = 0000 0000 0000 0000 0000 0000 0111 0001 0100 1111 0110 0011 1011 0000 0011 1110

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

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How to convert signed integers from decimal system to signed binary in two's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in two'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, keeping track of each remainder, until we get a quotient that is 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, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will 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 1s and all 1 bits with 0s (reversing the digits).
  • 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

  • 1. Start with the positive version of the number: |-60| = 60
  • 2. Divide repeatedly 60 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 60 ÷ 2 = 30 + 0
    • 30 ÷ 2 = 15 + 0
    • 15 ÷ 2 = 7 + 1
    • 7 ÷ 2 = 3 + 1
    • 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:
    60(10) = 11 1100(2)
  • 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
    60(10) = 0011 1100(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
    !(0011 1100) = 1100 0011
  • 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
    -60(10) = 1100 0011 + 1 = 1100 0100
  • Number -60(10), signed integer, converted from decimal system (base 10) to signed binary two's complement representation = 1100 0100