Convert 101 110 000 176 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 101 110 000 176(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
101 110 000 176 to a signed binary in one's (1'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.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 101 110 000 176 ÷ 2 = 50 555 000 088 + 0;
  • 50 555 000 088 ÷ 2 = 25 277 500 044 + 0;
  • 25 277 500 044 ÷ 2 = 12 638 750 022 + 0;
  • 12 638 750 022 ÷ 2 = 6 319 375 011 + 0;
  • 6 319 375 011 ÷ 2 = 3 159 687 505 + 1;
  • 3 159 687 505 ÷ 2 = 1 579 843 752 + 1;
  • 1 579 843 752 ÷ 2 = 789 921 876 + 0;
  • 789 921 876 ÷ 2 = 394 960 938 + 0;
  • 394 960 938 ÷ 2 = 197 480 469 + 0;
  • 197 480 469 ÷ 2 = 98 740 234 + 1;
  • 98 740 234 ÷ 2 = 49 370 117 + 0;
  • 49 370 117 ÷ 2 = 24 685 058 + 1;
  • 24 685 058 ÷ 2 = 12 342 529 + 0;
  • 12 342 529 ÷ 2 = 6 171 264 + 1;
  • 6 171 264 ÷ 2 = 3 085 632 + 0;
  • 3 085 632 ÷ 2 = 1 542 816 + 0;
  • 1 542 816 ÷ 2 = 771 408 + 0;
  • 771 408 ÷ 2 = 385 704 + 0;
  • 385 704 ÷ 2 = 192 852 + 0;
  • 192 852 ÷ 2 = 96 426 + 0;
  • 96 426 ÷ 2 = 48 213 + 0;
  • 48 213 ÷ 2 = 24 106 + 1;
  • 24 106 ÷ 2 = 12 053 + 0;
  • 12 053 ÷ 2 = 6 026 + 1;
  • 6 026 ÷ 2 = 3 013 + 0;
  • 3 013 ÷ 2 = 1 506 + 1;
  • 1 506 ÷ 2 = 753 + 0;
  • 753 ÷ 2 = 376 + 1;
  • 376 ÷ 2 = 188 + 0;
  • 188 ÷ 2 = 94 + 0;
  • 94 ÷ 2 = 47 + 0;
  • 47 ÷ 2 = 23 + 1;
  • 23 ÷ 2 = 11 + 1;
  • 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.

101 110 000 176(10) = 1 0111 1000 1010 1010 0000 0010 1010 0011 0000(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 101 110 000 176(10) converted to signed binary in one's complement representation:

101 110 000 176(10) = 0000 0000 0000 0000 0000 0000 0001 0111 1000 1010 1010 0000 0010 1010 0011 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 the decimal system to signed binary in one's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in one'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 that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to 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, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always 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 '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 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:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110