Convert 1 111 110 101 111 382 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 1 111 110 101 111 382(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
1 111 110 101 111 382 to a signed binary in two's (2'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.

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


  • division = quotient + remainder;
  • 1 111 110 101 111 382 ÷ 2 = 555 555 050 555 691 + 0;
  • 555 555 050 555 691 ÷ 2 = 277 777 525 277 845 + 1;
  • 277 777 525 277 845 ÷ 2 = 138 888 762 638 922 + 1;
  • 138 888 762 638 922 ÷ 2 = 69 444 381 319 461 + 0;
  • 69 444 381 319 461 ÷ 2 = 34 722 190 659 730 + 1;
  • 34 722 190 659 730 ÷ 2 = 17 361 095 329 865 + 0;
  • 17 361 095 329 865 ÷ 2 = 8 680 547 664 932 + 1;
  • 8 680 547 664 932 ÷ 2 = 4 340 273 832 466 + 0;
  • 4 340 273 832 466 ÷ 2 = 2 170 136 916 233 + 0;
  • 2 170 136 916 233 ÷ 2 = 1 085 068 458 116 + 1;
  • 1 085 068 458 116 ÷ 2 = 542 534 229 058 + 0;
  • 542 534 229 058 ÷ 2 = 271 267 114 529 + 0;
  • 271 267 114 529 ÷ 2 = 135 633 557 264 + 1;
  • 135 633 557 264 ÷ 2 = 67 816 778 632 + 0;
  • 67 816 778 632 ÷ 2 = 33 908 389 316 + 0;
  • 33 908 389 316 ÷ 2 = 16 954 194 658 + 0;
  • 16 954 194 658 ÷ 2 = 8 477 097 329 + 0;
  • 8 477 097 329 ÷ 2 = 4 238 548 664 + 1;
  • 4 238 548 664 ÷ 2 = 2 119 274 332 + 0;
  • 2 119 274 332 ÷ 2 = 1 059 637 166 + 0;
  • 1 059 637 166 ÷ 2 = 529 818 583 + 0;
  • 529 818 583 ÷ 2 = 264 909 291 + 1;
  • 264 909 291 ÷ 2 = 132 454 645 + 1;
  • 132 454 645 ÷ 2 = 66 227 322 + 1;
  • 66 227 322 ÷ 2 = 33 113 661 + 0;
  • 33 113 661 ÷ 2 = 16 556 830 + 1;
  • 16 556 830 ÷ 2 = 8 278 415 + 0;
  • 8 278 415 ÷ 2 = 4 139 207 + 1;
  • 4 139 207 ÷ 2 = 2 069 603 + 1;
  • 2 069 603 ÷ 2 = 1 034 801 + 1;
  • 1 034 801 ÷ 2 = 517 400 + 1;
  • 517 400 ÷ 2 = 258 700 + 0;
  • 258 700 ÷ 2 = 129 350 + 0;
  • 129 350 ÷ 2 = 64 675 + 0;
  • 64 675 ÷ 2 = 32 337 + 1;
  • 32 337 ÷ 2 = 16 168 + 1;
  • 16 168 ÷ 2 = 8 084 + 0;
  • 8 084 ÷ 2 = 4 042 + 0;
  • 4 042 ÷ 2 = 2 021 + 0;
  • 2 021 ÷ 2 = 1 010 + 1;
  • 1 010 ÷ 2 = 505 + 0;
  • 505 ÷ 2 = 252 + 1;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.

1 111 110 101 111 382(10) = 11 1111 0010 1000 1100 0111 1010 1110 0010 0001 0010 0101 0110(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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, 50,

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 1 111 110 101 111 382(10) converted to signed binary in two's complement representation:

1 111 110 101 111 382(10) = 0000 0000 0000 0011 1111 0010 1000 1100 0111 1010 1110 0010 0001 0010 0101 0110

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