Base ten decimal system signed integer number 647 288 676 734 782 converted to signed binary in one's complement representation

How to convert a signed integer in decimal system (in base 10):
647 288 676 734 782(10)
to a signed binary one's complement representation

1. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:

  • division = quotient + remainder;
  • 647 288 676 734 782 ÷ 2 = 323 644 338 367 391 + 0;
  • 323 644 338 367 391 ÷ 2 = 161 822 169 183 695 + 1;
  • 161 822 169 183 695 ÷ 2 = 80 911 084 591 847 + 1;
  • 80 911 084 591 847 ÷ 2 = 40 455 542 295 923 + 1;
  • 40 455 542 295 923 ÷ 2 = 20 227 771 147 961 + 1;
  • 20 227 771 147 961 ÷ 2 = 10 113 885 573 980 + 1;
  • 10 113 885 573 980 ÷ 2 = 5 056 942 786 990 + 0;
  • 5 056 942 786 990 ÷ 2 = 2 528 471 393 495 + 0;
  • 2 528 471 393 495 ÷ 2 = 1 264 235 696 747 + 1;
  • 1 264 235 696 747 ÷ 2 = 632 117 848 373 + 1;
  • 632 117 848 373 ÷ 2 = 316 058 924 186 + 1;
  • 316 058 924 186 ÷ 2 = 158 029 462 093 + 0;
  • 158 029 462 093 ÷ 2 = 79 014 731 046 + 1;
  • 79 014 731 046 ÷ 2 = 39 507 365 523 + 0;
  • 39 507 365 523 ÷ 2 = 19 753 682 761 + 1;
  • 19 753 682 761 ÷ 2 = 9 876 841 380 + 1;
  • 9 876 841 380 ÷ 2 = 4 938 420 690 + 0;
  • 4 938 420 690 ÷ 2 = 2 469 210 345 + 0;
  • 2 469 210 345 ÷ 2 = 1 234 605 172 + 1;
  • 1 234 605 172 ÷ 2 = 617 302 586 + 0;
  • 617 302 586 ÷ 2 = 308 651 293 + 0;
  • 308 651 293 ÷ 2 = 154 325 646 + 1;
  • 154 325 646 ÷ 2 = 77 162 823 + 0;
  • 77 162 823 ÷ 2 = 38 581 411 + 1;
  • 38 581 411 ÷ 2 = 19 290 705 + 1;
  • 19 290 705 ÷ 2 = 9 645 352 + 1;
  • 9 645 352 ÷ 2 = 4 822 676 + 0;
  • 4 822 676 ÷ 2 = 2 411 338 + 0;
  • 2 411 338 ÷ 2 = 1 205 669 + 0;
  • 1 205 669 ÷ 2 = 602 834 + 1;
  • 602 834 ÷ 2 = 301 417 + 0;
  • 301 417 ÷ 2 = 150 708 + 1;
  • 150 708 ÷ 2 = 75 354 + 0;
  • 75 354 ÷ 2 = 37 677 + 0;
  • 37 677 ÷ 2 = 18 838 + 1;
  • 18 838 ÷ 2 = 9 419 + 0;
  • 9 419 ÷ 2 = 4 709 + 1;
  • 4 709 ÷ 2 = 2 354 + 1;
  • 2 354 ÷ 2 = 1 177 + 0;
  • 1 177 ÷ 2 = 588 + 1;
  • 588 ÷ 2 = 294 + 0;
  • 294 ÷ 2 = 147 + 0;
  • 147 ÷ 2 = 73 + 1;
  • 73 ÷ 2 = 36 + 1;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:

647 288 676 734 782(10) = 10 0100 1100 1011 0100 1010 0011 1010 0100 1101 0111 0011 1110(2)

3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 50.

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 so that the first bit (leftmost) could be zero 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:

647 288 676 734 782(10) = 0000 0000 0000 0010 0100 1100 1011 0100 1010 0011 1010 0100 1101 0111 0011 1110

Conclusion:

Number 647 288 676 734 782, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:
647 288 676 734 782(10) = 0000 0000 0000 0010 0100 1100 1011 0100 1010 0011 1010 0100 1101 0111 0011 1110

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

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

How to convert a base ten 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 we get a quotient that is zero.

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 zero.

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

Latest signed integers 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