Convert 110 111 100 077 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

110 111 100 077(10) to a signed binary one's complement representation = ?

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;
  • 110 111 100 077 ÷ 2 = 55 055 550 038 + 1;
  • 55 055 550 038 ÷ 2 = 27 527 775 019 + 0;
  • 27 527 775 019 ÷ 2 = 13 763 887 509 + 1;
  • 13 763 887 509 ÷ 2 = 6 881 943 754 + 1;
  • 6 881 943 754 ÷ 2 = 3 440 971 877 + 0;
  • 3 440 971 877 ÷ 2 = 1 720 485 938 + 1;
  • 1 720 485 938 ÷ 2 = 860 242 969 + 0;
  • 860 242 969 ÷ 2 = 430 121 484 + 1;
  • 430 121 484 ÷ 2 = 215 060 742 + 0;
  • 215 060 742 ÷ 2 = 107 530 371 + 0;
  • 107 530 371 ÷ 2 = 53 765 185 + 1;
  • 53 765 185 ÷ 2 = 26 882 592 + 1;
  • 26 882 592 ÷ 2 = 13 441 296 + 0;
  • 13 441 296 ÷ 2 = 6 720 648 + 0;
  • 6 720 648 ÷ 2 = 3 360 324 + 0;
  • 3 360 324 ÷ 2 = 1 680 162 + 0;
  • 1 680 162 ÷ 2 = 840 081 + 0;
  • 840 081 ÷ 2 = 420 040 + 1;
  • 420 040 ÷ 2 = 210 020 + 0;
  • 210 020 ÷ 2 = 105 010 + 0;
  • 105 010 ÷ 2 = 52 505 + 0;
  • 52 505 ÷ 2 = 26 252 + 1;
  • 26 252 ÷ 2 = 13 126 + 0;
  • 13 126 ÷ 2 = 6 563 + 0;
  • 6 563 ÷ 2 = 3 281 + 1;
  • 3 281 ÷ 2 = 1 640 + 1;
  • 1 640 ÷ 2 = 820 + 0;
  • 820 ÷ 2 = 410 + 0;
  • 410 ÷ 2 = 205 + 0;
  • 205 ÷ 2 = 102 + 1;
  • 102 ÷ 2 = 51 + 0;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 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.

110 111 100 077(10) = 1 1001 1010 0011 0010 0010 0000 1100 1010 1101(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; ...

First bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

The least number that is:


a power of 2


and is larger than the actual length, 37,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


is: 64.


4. 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:

110 111 100 077(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1010 0011 0010 0010 0000 1100 1010 1101


Number 110 111 100 077, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

110 111 100 077(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1010 0011 0010 0010 0000 1100 1010 1101

Spaces used to group digits: for binary, by 4; for decimal, by 3.


More operations of this kind:

110 111 100 076 = ? | 110 111 100 078 = ?


Convert signed integer numbers from the decimal system (base ten) to signed binary one's complement representation

How to convert a base 10 signed integer number to signed binary in one's complement representation:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is 0.

2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.

3) Construct the positive binary computer representation so that the first bit is 0.

4) Only if the initial number is negative, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).

Latest signed integer numbers converted from decimal system to signed binary in one's complement representation

110,111,100,077 to signed binary one's complement = ? Apr 18 09:37 UTC (GMT)
4,564 to signed binary one's complement = ? Apr 18 09:36 UTC (GMT)
116,711,847 to signed binary one's complement = ? Apr 18 09:36 UTC (GMT)
-8,218 to signed binary one's complement = ? Apr 18 09:36 UTC (GMT)
101,010 to signed binary one's complement = ? Apr 18 09:36 UTC (GMT)
-670 to signed binary one's complement = ? Apr 18 09:34 UTC (GMT)
1,111,111,111,111,116 to signed binary one's complement = ? Apr 18 09:33 UTC (GMT)
-1,222 to signed binary one's complement = ? Apr 18 09:33 UTC (GMT)
111,131 to signed binary one's complement = ? Apr 18 09:33 UTC (GMT)
32,501 to signed binary one's complement = ? Apr 18 09:31 UTC (GMT)
127 to signed binary one's complement = ? Apr 18 09:31 UTC (GMT)
127 to signed binary one's complement = ? Apr 18 09:31 UTC (GMT)
99,999,995 to signed binary one's complement = ? Apr 18 09:30 UTC (GMT)
All decimal integer numbers converted to signed binary one's complement representation

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