Base ten decimal system signed integer number -2 169 359 905 902 365 506 converted to signed binary

How to convert the signed integer in decimal system (in base 10):
-2 169 359 905 902 365 506(10)
to a signed binary

1. We start with the positive version of the number:

|-2 169 359 905 902 365 506| = 2 169 359 905 902 365 506

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

  • division = quotient + remainder;
  • 2 169 359 905 902 365 506 ÷ 2 = 1 084 679 952 951 182 753 + 0;
  • 1 084 679 952 951 182 753 ÷ 2 = 542 339 976 475 591 376 + 1;
  • 542 339 976 475 591 376 ÷ 2 = 271 169 988 237 795 688 + 0;
  • 271 169 988 237 795 688 ÷ 2 = 135 584 994 118 897 844 + 0;
  • 135 584 994 118 897 844 ÷ 2 = 67 792 497 059 448 922 + 0;
  • 67 792 497 059 448 922 ÷ 2 = 33 896 248 529 724 461 + 0;
  • 33 896 248 529 724 461 ÷ 2 = 16 948 124 264 862 230 + 1;
  • 16 948 124 264 862 230 ÷ 2 = 8 474 062 132 431 115 + 0;
  • 8 474 062 132 431 115 ÷ 2 = 4 237 031 066 215 557 + 1;
  • 4 237 031 066 215 557 ÷ 2 = 2 118 515 533 107 778 + 1;
  • 2 118 515 533 107 778 ÷ 2 = 1 059 257 766 553 889 + 0;
  • 1 059 257 766 553 889 ÷ 2 = 529 628 883 276 944 + 1;
  • 529 628 883 276 944 ÷ 2 = 264 814 441 638 472 + 0;
  • 264 814 441 638 472 ÷ 2 = 132 407 220 819 236 + 0;
  • 132 407 220 819 236 ÷ 2 = 66 203 610 409 618 + 0;
  • 66 203 610 409 618 ÷ 2 = 33 101 805 204 809 + 0;
  • 33 101 805 204 809 ÷ 2 = 16 550 902 602 404 + 1;
  • 16 550 902 602 404 ÷ 2 = 8 275 451 301 202 + 0;
  • 8 275 451 301 202 ÷ 2 = 4 137 725 650 601 + 0;
  • 4 137 725 650 601 ÷ 2 = 2 068 862 825 300 + 1;
  • 2 068 862 825 300 ÷ 2 = 1 034 431 412 650 + 0;
  • 1 034 431 412 650 ÷ 2 = 517 215 706 325 + 0;
  • 517 215 706 325 ÷ 2 = 258 607 853 162 + 1;
  • 258 607 853 162 ÷ 2 = 129 303 926 581 + 0;
  • 129 303 926 581 ÷ 2 = 64 651 963 290 + 1;
  • 64 651 963 290 ÷ 2 = 32 325 981 645 + 0;
  • 32 325 981 645 ÷ 2 = 16 162 990 822 + 1;
  • 16 162 990 822 ÷ 2 = 8 081 495 411 + 0;
  • 8 081 495 411 ÷ 2 = 4 040 747 705 + 1;
  • 4 040 747 705 ÷ 2 = 2 020 373 852 + 1;
  • 2 020 373 852 ÷ 2 = 1 010 186 926 + 0;
  • 1 010 186 926 ÷ 2 = 505 093 463 + 0;
  • 505 093 463 ÷ 2 = 252 546 731 + 1;
  • 252 546 731 ÷ 2 = 126 273 365 + 1;
  • 126 273 365 ÷ 2 = 63 136 682 + 1;
  • 63 136 682 ÷ 2 = 31 568 341 + 0;
  • 31 568 341 ÷ 2 = 15 784 170 + 1;
  • 15 784 170 ÷ 2 = 7 892 085 + 0;
  • 7 892 085 ÷ 2 = 3 946 042 + 1;
  • 3 946 042 ÷ 2 = 1 973 021 + 0;
  • 1 973 021 ÷ 2 = 986 510 + 1;
  • 986 510 ÷ 2 = 493 255 + 0;
  • 493 255 ÷ 2 = 246 627 + 1;
  • 246 627 ÷ 2 = 123 313 + 1;
  • 123 313 ÷ 2 = 61 656 + 1;
  • 61 656 ÷ 2 = 30 828 + 0;
  • 30 828 ÷ 2 = 15 414 + 0;
  • 15 414 ÷ 2 = 7 707 + 0;
  • 7 707 ÷ 2 = 3 853 + 1;
  • 3 853 ÷ 2 = 1 926 + 1;
  • 1 926 ÷ 2 = 963 + 0;
  • 963 ÷ 2 = 481 + 1;
  • 481 ÷ 2 = 240 + 1;
  • 240 ÷ 2 = 120 + 0;
  • 120 ÷ 2 = 60 + 0;
  • 60 ÷ 2 = 30 + 0;
  • 30 ÷ 2 = 15 + 0;
  • 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:

2 169 359 905 902 365 506(10) = 1 1110 0001 1011 0001 1101 0101 0111 0011 0101 0100 1001 0000 1011 0100 0010(2)

4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 61.

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.

5. 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:

2 169 359 905 902 365 506(10) = 0001 1110 0001 1011 0001 1101 0101 0111 0011 0101 0100 1001 0000 1011 0100 0010

6. To get the negative integer number representation change the first bit (the leftmost), from 0 to 1:

-2 169 359 905 902 365 506(10) = 1001 1110 0001 1011 0001 1101 0101 0111 0011 0101 0100 1001 0000 1011 0100 0010

Conclusion:

Number -2 169 359 905 902 365 506, a signed integer, converted from decimal system (base 10) to signed binary:
-2 169 359 905 902 365 506(10) = 1001 1110 0001 1011 0001 1101 0101 0111 0011 0101 0100 1001 0000 1011 0100 0010

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