Convert 100 111 000 100 092 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):
100 111 000 100 092(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;
  • 100 111 000 100 092 ÷ 2 = 50 055 500 050 046 + 0;
  • 50 055 500 050 046 ÷ 2 = 25 027 750 025 023 + 0;
  • 25 027 750 025 023 ÷ 2 = 12 513 875 012 511 + 1;
  • 12 513 875 012 511 ÷ 2 = 6 256 937 506 255 + 1;
  • 6 256 937 506 255 ÷ 2 = 3 128 468 753 127 + 1;
  • 3 128 468 753 127 ÷ 2 = 1 564 234 376 563 + 1;
  • 1 564 234 376 563 ÷ 2 = 782 117 188 281 + 1;
  • 782 117 188 281 ÷ 2 = 391 058 594 140 + 1;
  • 391 058 594 140 ÷ 2 = 195 529 297 070 + 0;
  • 195 529 297 070 ÷ 2 = 97 764 648 535 + 0;
  • 97 764 648 535 ÷ 2 = 48 882 324 267 + 1;
  • 48 882 324 267 ÷ 2 = 24 441 162 133 + 1;
  • 24 441 162 133 ÷ 2 = 12 220 581 066 + 1;
  • 12 220 581 066 ÷ 2 = 6 110 290 533 + 0;
  • 6 110 290 533 ÷ 2 = 3 055 145 266 + 1;
  • 3 055 145 266 ÷ 2 = 1 527 572 633 + 0;
  • 1 527 572 633 ÷ 2 = 763 786 316 + 1;
  • 763 786 316 ÷ 2 = 381 893 158 + 0;
  • 381 893 158 ÷ 2 = 190 946 579 + 0;
  • 190 946 579 ÷ 2 = 95 473 289 + 1;
  • 95 473 289 ÷ 2 = 47 736 644 + 1;
  • 47 736 644 ÷ 2 = 23 868 322 + 0;
  • 23 868 322 ÷ 2 = 11 934 161 + 0;
  • 11 934 161 ÷ 2 = 5 967 080 + 1;
  • 5 967 080 ÷ 2 = 2 983 540 + 0;
  • 2 983 540 ÷ 2 = 1 491 770 + 0;
  • 1 491 770 ÷ 2 = 745 885 + 0;
  • 745 885 ÷ 2 = 372 942 + 1;
  • 372 942 ÷ 2 = 186 471 + 0;
  • 186 471 ÷ 2 = 93 235 + 1;
  • 93 235 ÷ 2 = 46 617 + 1;
  • 46 617 ÷ 2 = 23 308 + 1;
  • 23 308 ÷ 2 = 11 654 + 0;
  • 11 654 ÷ 2 = 5 827 + 0;
  • 5 827 ÷ 2 = 2 913 + 1;
  • 2 913 ÷ 2 = 1 456 + 1;
  • 1 456 ÷ 2 = 728 + 0;
  • 728 ÷ 2 = 364 + 0;
  • 364 ÷ 2 = 182 + 0;
  • 182 ÷ 2 = 91 + 0;
  • 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.

100 111 000 100 092(10) = 101 1011 0000 1100 1110 1000 1001 1001 0101 1100 1111 1100(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; ...

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, 47,


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:

100 111 000 100 092(10) = 0000 0000 0000 0000 0101 1011 0000 1100 1110 1000 1001 1001 0101 1100 1111 1100


Conclusion:

Number 100 111 000 100 092, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

100 111 000 100 092(10) = 0000 0000 0000 0000 0101 1011 0000 1100 1110 1000 1001 1001 0101 1100 1111 1100

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


More operations of this kind:

100 111 000 100 091 = ? | 100 111 000 100 093 = ?


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

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