Convert 1 100 011 010 110 841 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 1 100 011 010 110 841(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
1 100 011 010 110 841 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;
  • 1 100 011 010 110 841 ÷ 2 = 550 005 505 055 420 + 1;
  • 550 005 505 055 420 ÷ 2 = 275 002 752 527 710 + 0;
  • 275 002 752 527 710 ÷ 2 = 137 501 376 263 855 + 0;
  • 137 501 376 263 855 ÷ 2 = 68 750 688 131 927 + 1;
  • 68 750 688 131 927 ÷ 2 = 34 375 344 065 963 + 1;
  • 34 375 344 065 963 ÷ 2 = 17 187 672 032 981 + 1;
  • 17 187 672 032 981 ÷ 2 = 8 593 836 016 490 + 1;
  • 8 593 836 016 490 ÷ 2 = 4 296 918 008 245 + 0;
  • 4 296 918 008 245 ÷ 2 = 2 148 459 004 122 + 1;
  • 2 148 459 004 122 ÷ 2 = 1 074 229 502 061 + 0;
  • 1 074 229 502 061 ÷ 2 = 537 114 751 030 + 1;
  • 537 114 751 030 ÷ 2 = 268 557 375 515 + 0;
  • 268 557 375 515 ÷ 2 = 134 278 687 757 + 1;
  • 134 278 687 757 ÷ 2 = 67 139 343 878 + 1;
  • 67 139 343 878 ÷ 2 = 33 569 671 939 + 0;
  • 33 569 671 939 ÷ 2 = 16 784 835 969 + 1;
  • 16 784 835 969 ÷ 2 = 8 392 417 984 + 1;
  • 8 392 417 984 ÷ 2 = 4 196 208 992 + 0;
  • 4 196 208 992 ÷ 2 = 2 098 104 496 + 0;
  • 2 098 104 496 ÷ 2 = 1 049 052 248 + 0;
  • 1 049 052 248 ÷ 2 = 524 526 124 + 0;
  • 524 526 124 ÷ 2 = 262 263 062 + 0;
  • 262 263 062 ÷ 2 = 131 131 531 + 0;
  • 131 131 531 ÷ 2 = 65 565 765 + 1;
  • 65 565 765 ÷ 2 = 32 782 882 + 1;
  • 32 782 882 ÷ 2 = 16 391 441 + 0;
  • 16 391 441 ÷ 2 = 8 195 720 + 1;
  • 8 195 720 ÷ 2 = 4 097 860 + 0;
  • 4 097 860 ÷ 2 = 2 048 930 + 0;
  • 2 048 930 ÷ 2 = 1 024 465 + 0;
  • 1 024 465 ÷ 2 = 512 232 + 1;
  • 512 232 ÷ 2 = 256 116 + 0;
  • 256 116 ÷ 2 = 128 058 + 0;
  • 128 058 ÷ 2 = 64 029 + 0;
  • 64 029 ÷ 2 = 32 014 + 1;
  • 32 014 ÷ 2 = 16 007 + 0;
  • 16 007 ÷ 2 = 8 003 + 1;
  • 8 003 ÷ 2 = 4 001 + 1;
  • 4 001 ÷ 2 = 2 000 + 1;
  • 2 000 ÷ 2 = 1 000 + 0;
  • 1 000 ÷ 2 = 500 + 0;
  • 500 ÷ 2 = 250 + 0;
  • 250 ÷ 2 = 125 + 0;
  • 125 ÷ 2 = 62 + 1;
  • 62 ÷ 2 = 31 + 0;
  • 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.

1 100 011 010 110 841(10) = 11 1110 1000 0111 0100 0100 0101 1000 0001 1011 0101 0111 1001(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 1 100 011 010 110 841(10) converted to signed binary in two's complement representation:

1 100 011 010 110 841(10) = 0000 0000 0000 0011 1110 1000 0111 0100 0100 0101 1000 0001 1011 0101 0111 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