Base ten decimal system signed integer number 1 000 111 100 011 111 converted to signed binary

How to convert the signed integer in decimal system (in base 10):
1 000 111 100 011 111(10)
to a signed binary

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;
  • 1 000 111 100 011 111 ÷ 2 = 500 055 550 005 555 + 1;
  • 500 055 550 005 555 ÷ 2 = 250 027 775 002 777 + 1;
  • 250 027 775 002 777 ÷ 2 = 125 013 887 501 388 + 1;
  • 125 013 887 501 388 ÷ 2 = 62 506 943 750 694 + 0;
  • 62 506 943 750 694 ÷ 2 = 31 253 471 875 347 + 0;
  • 31 253 471 875 347 ÷ 2 = 15 626 735 937 673 + 1;
  • 15 626 735 937 673 ÷ 2 = 7 813 367 968 836 + 1;
  • 7 813 367 968 836 ÷ 2 = 3 906 683 984 418 + 0;
  • 3 906 683 984 418 ÷ 2 = 1 953 341 992 209 + 0;
  • 1 953 341 992 209 ÷ 2 = 976 670 996 104 + 1;
  • 976 670 996 104 ÷ 2 = 488 335 498 052 + 0;
  • 488 335 498 052 ÷ 2 = 244 167 749 026 + 0;
  • 244 167 749 026 ÷ 2 = 122 083 874 513 + 0;
  • 122 083 874 513 ÷ 2 = 61 041 937 256 + 1;
  • 61 041 937 256 ÷ 2 = 30 520 968 628 + 0;
  • 30 520 968 628 ÷ 2 = 15 260 484 314 + 0;
  • 15 260 484 314 ÷ 2 = 7 630 242 157 + 0;
  • 7 630 242 157 ÷ 2 = 3 815 121 078 + 1;
  • 3 815 121 078 ÷ 2 = 1 907 560 539 + 0;
  • 1 907 560 539 ÷ 2 = 953 780 269 + 1;
  • 953 780 269 ÷ 2 = 476 890 134 + 1;
  • 476 890 134 ÷ 2 = 238 445 067 + 0;
  • 238 445 067 ÷ 2 = 119 222 533 + 1;
  • 119 222 533 ÷ 2 = 59 611 266 + 1;
  • 59 611 266 ÷ 2 = 29 805 633 + 0;
  • 29 805 633 ÷ 2 = 14 902 816 + 1;
  • 14 902 816 ÷ 2 = 7 451 408 + 0;
  • 7 451 408 ÷ 2 = 3 725 704 + 0;
  • 3 725 704 ÷ 2 = 1 862 852 + 0;
  • 1 862 852 ÷ 2 = 931 426 + 0;
  • 931 426 ÷ 2 = 465 713 + 0;
  • 465 713 ÷ 2 = 232 856 + 1;
  • 232 856 ÷ 2 = 116 428 + 0;
  • 116 428 ÷ 2 = 58 214 + 0;
  • 58 214 ÷ 2 = 29 107 + 0;
  • 29 107 ÷ 2 = 14 553 + 1;
  • 14 553 ÷ 2 = 7 276 + 1;
  • 7 276 ÷ 2 = 3 638 + 0;
  • 3 638 ÷ 2 = 1 819 + 0;
  • 1 819 ÷ 2 = 909 + 1;
  • 909 ÷ 2 = 454 + 1;
  • 454 ÷ 2 = 227 + 0;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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:

1 000 111 100 011 111(10) = 11 1000 1101 1001 1000 1000 0010 1101 1010 0010 0010 0110 0111(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) is reserved for the sign:
0 = positive integer number, 1 = negative integer number

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:

1 000 111 100 011 111(10) = 0000 0000 0000 0011 1000 1101 1001 1000 1000 0010 1101 1010 0010 0010 0110 0111

Conclusion:

Number 1 000 111 100 011 111, a signed integer, converted from decimal system (base 10) to signed binary:
1 000 111 100 011 111(10) = 0000 0000 0000 0011 1000 1101 1001 1000 1000 0010 1101 1010 0010 0010 0110 0111

First bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number


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

How to convert a base ten signed integer number to signed binary:

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, change the first bit (the leftmost), from 0 to 1. The leftmost bit is reserved for the sign, 1 = negative, 0 = positive.

Latest signed integers numbers converted from decimal (base ten) to signed binary

How to convert signed integers from decimal system to binary code system

Follow the steps below to convert a signed base ten integer number to signed binary:

  • 1. In a signed binary, first bit (the leftmost) is reserved for sign: 0 = positive integer number, 1 = positive integer number. If the number to be converted is negative, start with its positive version.
  • 2. Divide repeatedly by 2 the positive integer number keeping track of each remainder. STOP when we get a quotient that is 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 have a length of 4, 8, 16, 32, 64, ... bits (power of 2) - if needed, fill in extra '0' bits in front of the base 2 number (to the left), up to the right length; this way the first bit (the leftmost one) is always '0', as for a positive representation.
  • 5. To get the negative reprezentation of the number, simply switch the first bit (the leftmost one), from '0' to '1'.

Example: convert the negative number -63 from decimal system (base ten) to signed binary code system:

  • 1. Start with the positive version of the number: |-63| = 63;
  • 2. Divide repeatedly 63 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder
    • 63 ÷ 2 = 31 + 1
    • 31 ÷ 2 = 15 + 1
    • 15 ÷ 2 = 7 + 1
    • 7 ÷ 2 = 3 + 1
    • 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:
    63(10) = 11 1111(2)
  • 4. The actual length of base 2 representation number is 6, so the positive binary computer representation length of the signed binary will take in this case 8 bits (the least power of 2 higher than 6) - add extra '0's in front (to the left), up to the required length; this way the first bit (the leftmost one) is to be '0', as for a positive number:
    63(10) = 0011 1111(2)
  • 5. To get the negative integer number representation simply change the first bit (the leftmost), from '0' to '1':
    -63(10) = 1011 1111
  • Number -63(10), signed integer, converted from decimal system (base 10) to signed binary = 1011 1111