Convert 101 010 111 000 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

How to convert a signed integer in decimal system (in base 10):
101 010 111 000(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;
  • 101 010 111 000 ÷ 2 = 50 505 055 500 + 0;
  • 50 505 055 500 ÷ 2 = 25 252 527 750 + 0;
  • 25 252 527 750 ÷ 2 = 12 626 263 875 + 0;
  • 12 626 263 875 ÷ 2 = 6 313 131 937 + 1;
  • 6 313 131 937 ÷ 2 = 3 156 565 968 + 1;
  • 3 156 565 968 ÷ 2 = 1 578 282 984 + 0;
  • 1 578 282 984 ÷ 2 = 789 141 492 + 0;
  • 789 141 492 ÷ 2 = 394 570 746 + 0;
  • 394 570 746 ÷ 2 = 197 285 373 + 0;
  • 197 285 373 ÷ 2 = 98 642 686 + 1;
  • 98 642 686 ÷ 2 = 49 321 343 + 0;
  • 49 321 343 ÷ 2 = 24 660 671 + 1;
  • 24 660 671 ÷ 2 = 12 330 335 + 1;
  • 12 330 335 ÷ 2 = 6 165 167 + 1;
  • 6 165 167 ÷ 2 = 3 082 583 + 1;
  • 3 082 583 ÷ 2 = 1 541 291 + 1;
  • 1 541 291 ÷ 2 = 770 645 + 1;
  • 770 645 ÷ 2 = 385 322 + 1;
  • 385 322 ÷ 2 = 192 661 + 0;
  • 192 661 ÷ 2 = 96 330 + 1;
  • 96 330 ÷ 2 = 48 165 + 0;
  • 48 165 ÷ 2 = 24 082 + 1;
  • 24 082 ÷ 2 = 12 041 + 0;
  • 12 041 ÷ 2 = 6 020 + 1;
  • 6 020 ÷ 2 = 3 010 + 0;
  • 3 010 ÷ 2 = 1 505 + 0;
  • 1 505 ÷ 2 = 752 + 1;
  • 752 ÷ 2 = 376 + 0;
  • 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.

101 010 111 000(10) = 1 0111 1000 0100 1010 1011 1111 1010 0001 1000(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:

101 010 111 000(10) = 0000 0000 0000 0000 0000 0000 0001 0111 1000 0100 1010 1011 1111 1010 0001 1000


Conclusion:

Number 101 010 111 000, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

101 010 111 000(10) = 0000 0000 0000 0000 0000 0000 0001 0111 1000 0100 1010 1011 1111 1010 0001 1000

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


More operations of this kind:

101 010 110 999 = ? | 101 010 111 001 = ?


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

101,010,111,000 to signed binary one's complement = ? Jan 26 17:21 UTC (GMT)
-27,647 to signed binary one's complement = ? Jan 26 17:19 UTC (GMT)
-6 to signed binary one's complement = ? Jan 26 17:18 UTC (GMT)
-6 to signed binary one's complement = ? Jan 26 17:18 UTC (GMT)
29 to signed binary one's complement = ? Jan 26 17:17 UTC (GMT)
1,011,110,100,101,011 to signed binary one's complement = ? Jan 26 17:16 UTC (GMT)
-2,453 to signed binary one's complement = ? Jan 26 17:16 UTC (GMT)
10,000,985 to signed binary one's complement = ? Jan 26 17:15 UTC (GMT)
1,111,010,000,001,104 to signed binary one's complement = ? Jan 26 17:13 UTC (GMT)
3,486 to signed binary one's complement = ? Jan 26 17:13 UTC (GMT)
1,364,098,225 to signed binary one's complement = ? Jan 26 17:11 UTC (GMT)
-11,010,095 to signed binary one's complement = ? Jan 26 17:11 UTC (GMT)
22,037 to signed binary one's complement = ? Jan 26 17:11 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