Convert 1 101 010 111 100 069 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 1 101 010 111 100 069(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
1 101 010 111 100 069 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;
  • 1 101 010 111 100 069 ÷ 2 = 550 505 055 550 034 + 1;
  • 550 505 055 550 034 ÷ 2 = 275 252 527 775 017 + 0;
  • 275 252 527 775 017 ÷ 2 = 137 626 263 887 508 + 1;
  • 137 626 263 887 508 ÷ 2 = 68 813 131 943 754 + 0;
  • 68 813 131 943 754 ÷ 2 = 34 406 565 971 877 + 0;
  • 34 406 565 971 877 ÷ 2 = 17 203 282 985 938 + 1;
  • 17 203 282 985 938 ÷ 2 = 8 601 641 492 969 + 0;
  • 8 601 641 492 969 ÷ 2 = 4 300 820 746 484 + 1;
  • 4 300 820 746 484 ÷ 2 = 2 150 410 373 242 + 0;
  • 2 150 410 373 242 ÷ 2 = 1 075 205 186 621 + 0;
  • 1 075 205 186 621 ÷ 2 = 537 602 593 310 + 1;
  • 537 602 593 310 ÷ 2 = 268 801 296 655 + 0;
  • 268 801 296 655 ÷ 2 = 134 400 648 327 + 1;
  • 134 400 648 327 ÷ 2 = 67 200 324 163 + 1;
  • 67 200 324 163 ÷ 2 = 33 600 162 081 + 1;
  • 33 600 162 081 ÷ 2 = 16 800 081 040 + 1;
  • 16 800 081 040 ÷ 2 = 8 400 040 520 + 0;
  • 8 400 040 520 ÷ 2 = 4 200 020 260 + 0;
  • 4 200 020 260 ÷ 2 = 2 100 010 130 + 0;
  • 2 100 010 130 ÷ 2 = 1 050 005 065 + 0;
  • 1 050 005 065 ÷ 2 = 525 002 532 + 1;
  • 525 002 532 ÷ 2 = 262 501 266 + 0;
  • 262 501 266 ÷ 2 = 131 250 633 + 0;
  • 131 250 633 ÷ 2 = 65 625 316 + 1;
  • 65 625 316 ÷ 2 = 32 812 658 + 0;
  • 32 812 658 ÷ 2 = 16 406 329 + 0;
  • 16 406 329 ÷ 2 = 8 203 164 + 1;
  • 8 203 164 ÷ 2 = 4 101 582 + 0;
  • 4 101 582 ÷ 2 = 2 050 791 + 0;
  • 2 050 791 ÷ 2 = 1 025 395 + 1;
  • 1 025 395 ÷ 2 = 512 697 + 1;
  • 512 697 ÷ 2 = 256 348 + 1;
  • 256 348 ÷ 2 = 128 174 + 0;
  • 128 174 ÷ 2 = 64 087 + 0;
  • 64 087 ÷ 2 = 32 043 + 1;
  • 32 043 ÷ 2 = 16 021 + 1;
  • 16 021 ÷ 2 = 8 010 + 1;
  • 8 010 ÷ 2 = 4 005 + 0;
  • 4 005 ÷ 2 = 2 002 + 1;
  • 2 002 ÷ 2 = 1 001 + 0;
  • 1 001 ÷ 2 = 500 + 1;
  • 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.

1 101 010 111 100 069(10) = 11 1110 1001 0101 1100 1110 0100 1001 0000 1111 0100 1010 0101(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 1 101 010 111 100 069(10) converted to signed binary in two's complement representation:

1 101 010 111 100 069(10) = 0000 0000 0000 0011 1110 1001 0101 1100 1110 0100 1001 0000 1111 0100 1010 0101

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