Convert 101 100 101 101 376 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 101 100 101 101 376(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
101 100 101 101 376 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;
  • 101 100 101 101 376 ÷ 2 = 50 550 050 550 688 + 0;
  • 50 550 050 550 688 ÷ 2 = 25 275 025 275 344 + 0;
  • 25 275 025 275 344 ÷ 2 = 12 637 512 637 672 + 0;
  • 12 637 512 637 672 ÷ 2 = 6 318 756 318 836 + 0;
  • 6 318 756 318 836 ÷ 2 = 3 159 378 159 418 + 0;
  • 3 159 378 159 418 ÷ 2 = 1 579 689 079 709 + 0;
  • 1 579 689 079 709 ÷ 2 = 789 844 539 854 + 1;
  • 789 844 539 854 ÷ 2 = 394 922 269 927 + 0;
  • 394 922 269 927 ÷ 2 = 197 461 134 963 + 1;
  • 197 461 134 963 ÷ 2 = 98 730 567 481 + 1;
  • 98 730 567 481 ÷ 2 = 49 365 283 740 + 1;
  • 49 365 283 740 ÷ 2 = 24 682 641 870 + 0;
  • 24 682 641 870 ÷ 2 = 12 341 320 935 + 0;
  • 12 341 320 935 ÷ 2 = 6 170 660 467 + 1;
  • 6 170 660 467 ÷ 2 = 3 085 330 233 + 1;
  • 3 085 330 233 ÷ 2 = 1 542 665 116 + 1;
  • 1 542 665 116 ÷ 2 = 771 332 558 + 0;
  • 771 332 558 ÷ 2 = 385 666 279 + 0;
  • 385 666 279 ÷ 2 = 192 833 139 + 1;
  • 192 833 139 ÷ 2 = 96 416 569 + 1;
  • 96 416 569 ÷ 2 = 48 208 284 + 1;
  • 48 208 284 ÷ 2 = 24 104 142 + 0;
  • 24 104 142 ÷ 2 = 12 052 071 + 0;
  • 12 052 071 ÷ 2 = 6 026 035 + 1;
  • 6 026 035 ÷ 2 = 3 013 017 + 1;
  • 3 013 017 ÷ 2 = 1 506 508 + 1;
  • 1 506 508 ÷ 2 = 753 254 + 0;
  • 753 254 ÷ 2 = 376 627 + 0;
  • 376 627 ÷ 2 = 188 313 + 1;
  • 188 313 ÷ 2 = 94 156 + 1;
  • 94 156 ÷ 2 = 47 078 + 0;
  • 47 078 ÷ 2 = 23 539 + 0;
  • 23 539 ÷ 2 = 11 769 + 1;
  • 11 769 ÷ 2 = 5 884 + 1;
  • 5 884 ÷ 2 = 2 942 + 0;
  • 2 942 ÷ 2 = 1 471 + 0;
  • 1 471 ÷ 2 = 735 + 1;
  • 735 ÷ 2 = 367 + 1;
  • 367 ÷ 2 = 183 + 1;
  • 183 ÷ 2 = 91 + 1;
  • 91 ÷ 2 = 45 + 1;
  • 45 ÷ 2 = 22 + 1;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 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.

101 100 101 101 376(10) = 101 1011 1111 0011 0011 0011 1001 1100 1110 0111 0100 0000(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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, 47,

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 101 100 101 101 376(10) converted to signed binary in two's complement representation:

101 100 101 101 376(10) = 0000 0000 0000 0000 0101 1011 1111 0011 0011 0011 1001 1100 1110 0111 0100 0000

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