Convert 110 001 100 601 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 110 001 100 601(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
110 001 100 601 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;
  • 110 001 100 601 ÷ 2 = 55 000 550 300 + 1;
  • 55 000 550 300 ÷ 2 = 27 500 275 150 + 0;
  • 27 500 275 150 ÷ 2 = 13 750 137 575 + 0;
  • 13 750 137 575 ÷ 2 = 6 875 068 787 + 1;
  • 6 875 068 787 ÷ 2 = 3 437 534 393 + 1;
  • 3 437 534 393 ÷ 2 = 1 718 767 196 + 1;
  • 1 718 767 196 ÷ 2 = 859 383 598 + 0;
  • 859 383 598 ÷ 2 = 429 691 799 + 0;
  • 429 691 799 ÷ 2 = 214 845 899 + 1;
  • 214 845 899 ÷ 2 = 107 422 949 + 1;
  • 107 422 949 ÷ 2 = 53 711 474 + 1;
  • 53 711 474 ÷ 2 = 26 855 737 + 0;
  • 26 855 737 ÷ 2 = 13 427 868 + 1;
  • 13 427 868 ÷ 2 = 6 713 934 + 0;
  • 6 713 934 ÷ 2 = 3 356 967 + 0;
  • 3 356 967 ÷ 2 = 1 678 483 + 1;
  • 1 678 483 ÷ 2 = 839 241 + 1;
  • 839 241 ÷ 2 = 419 620 + 1;
  • 419 620 ÷ 2 = 209 810 + 0;
  • 209 810 ÷ 2 = 104 905 + 0;
  • 104 905 ÷ 2 = 52 452 + 1;
  • 52 452 ÷ 2 = 26 226 + 0;
  • 26 226 ÷ 2 = 13 113 + 0;
  • 13 113 ÷ 2 = 6 556 + 1;
  • 6 556 ÷ 2 = 3 278 + 0;
  • 3 278 ÷ 2 = 1 639 + 0;
  • 1 639 ÷ 2 = 819 + 1;
  • 819 ÷ 2 = 409 + 1;
  • 409 ÷ 2 = 204 + 1;
  • 204 ÷ 2 = 102 + 0;
  • 102 ÷ 2 = 51 + 0;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 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.

110 001 100 601(10) = 1 1001 1001 1100 1001 0011 1001 0111 0011 1001(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 37.

  • 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, 37,

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 110 001 100 601(10) converted to signed binary in two's complement representation:

110 001 100 601(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1001 1100 1001 0011 1001 0111 0011 1001

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