Convert 11 010 001 101 010 270 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 11 010 001 101 010 270(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
11 010 001 101 010 270 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;
  • 11 010 001 101 010 270 ÷ 2 = 5 505 000 550 505 135 + 0;
  • 5 505 000 550 505 135 ÷ 2 = 2 752 500 275 252 567 + 1;
  • 2 752 500 275 252 567 ÷ 2 = 1 376 250 137 626 283 + 1;
  • 1 376 250 137 626 283 ÷ 2 = 688 125 068 813 141 + 1;
  • 688 125 068 813 141 ÷ 2 = 344 062 534 406 570 + 1;
  • 344 062 534 406 570 ÷ 2 = 172 031 267 203 285 + 0;
  • 172 031 267 203 285 ÷ 2 = 86 015 633 601 642 + 1;
  • 86 015 633 601 642 ÷ 2 = 43 007 816 800 821 + 0;
  • 43 007 816 800 821 ÷ 2 = 21 503 908 400 410 + 1;
  • 21 503 908 400 410 ÷ 2 = 10 751 954 200 205 + 0;
  • 10 751 954 200 205 ÷ 2 = 5 375 977 100 102 + 1;
  • 5 375 977 100 102 ÷ 2 = 2 687 988 550 051 + 0;
  • 2 687 988 550 051 ÷ 2 = 1 343 994 275 025 + 1;
  • 1 343 994 275 025 ÷ 2 = 671 997 137 512 + 1;
  • 671 997 137 512 ÷ 2 = 335 998 568 756 + 0;
  • 335 998 568 756 ÷ 2 = 167 999 284 378 + 0;
  • 167 999 284 378 ÷ 2 = 83 999 642 189 + 0;
  • 83 999 642 189 ÷ 2 = 41 999 821 094 + 1;
  • 41 999 821 094 ÷ 2 = 20 999 910 547 + 0;
  • 20 999 910 547 ÷ 2 = 10 499 955 273 + 1;
  • 10 499 955 273 ÷ 2 = 5 249 977 636 + 1;
  • 5 249 977 636 ÷ 2 = 2 624 988 818 + 0;
  • 2 624 988 818 ÷ 2 = 1 312 494 409 + 0;
  • 1 312 494 409 ÷ 2 = 656 247 204 + 1;
  • 656 247 204 ÷ 2 = 328 123 602 + 0;
  • 328 123 602 ÷ 2 = 164 061 801 + 0;
  • 164 061 801 ÷ 2 = 82 030 900 + 1;
  • 82 030 900 ÷ 2 = 41 015 450 + 0;
  • 41 015 450 ÷ 2 = 20 507 725 + 0;
  • 20 507 725 ÷ 2 = 10 253 862 + 1;
  • 10 253 862 ÷ 2 = 5 126 931 + 0;
  • 5 126 931 ÷ 2 = 2 563 465 + 1;
  • 2 563 465 ÷ 2 = 1 281 732 + 1;
  • 1 281 732 ÷ 2 = 640 866 + 0;
  • 640 866 ÷ 2 = 320 433 + 0;
  • 320 433 ÷ 2 = 160 216 + 1;
  • 160 216 ÷ 2 = 80 108 + 0;
  • 80 108 ÷ 2 = 40 054 + 0;
  • 40 054 ÷ 2 = 20 027 + 0;
  • 20 027 ÷ 2 = 10 013 + 1;
  • 10 013 ÷ 2 = 5 006 + 1;
  • 5 006 ÷ 2 = 2 503 + 0;
  • 2 503 ÷ 2 = 1 251 + 1;
  • 1 251 ÷ 2 = 625 + 1;
  • 625 ÷ 2 = 312 + 1;
  • 312 ÷ 2 = 156 + 0;
  • 156 ÷ 2 = 78 + 0;
  • 78 ÷ 2 = 39 + 0;
  • 39 ÷ 2 = 19 + 1;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 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.

11 010 001 101 010 270(10) = 10 0111 0001 1101 1000 1001 1010 0100 1001 1010 0011 0101 0101 1110(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 54.

  • 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, 54,

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 11 010 001 101 010 270(10) converted to signed binary in two's complement representation:

11 010 001 101 010 270(10) = 0000 0000 0010 0111 0001 1101 1000 1001 1010 0100 1001 1010 0011 0101 0101 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