Signed: Integer ↗ Binary: 155 646 546 578 786 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number 155 646 546 578 786(10)
converted and written as a signed binary (base 2) = ?

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;
  • 155 646 546 578 786 ÷ 2 = 77 823 273 289 393 + 0;
  • 77 823 273 289 393 ÷ 2 = 38 911 636 644 696 + 1;
  • 38 911 636 644 696 ÷ 2 = 19 455 818 322 348 + 0;
  • 19 455 818 322 348 ÷ 2 = 9 727 909 161 174 + 0;
  • 9 727 909 161 174 ÷ 2 = 4 863 954 580 587 + 0;
  • 4 863 954 580 587 ÷ 2 = 2 431 977 290 293 + 1;
  • 2 431 977 290 293 ÷ 2 = 1 215 988 645 146 + 1;
  • 1 215 988 645 146 ÷ 2 = 607 994 322 573 + 0;
  • 607 994 322 573 ÷ 2 = 303 997 161 286 + 1;
  • 303 997 161 286 ÷ 2 = 151 998 580 643 + 0;
  • 151 998 580 643 ÷ 2 = 75 999 290 321 + 1;
  • 75 999 290 321 ÷ 2 = 37 999 645 160 + 1;
  • 37 999 645 160 ÷ 2 = 18 999 822 580 + 0;
  • 18 999 822 580 ÷ 2 = 9 499 911 290 + 0;
  • 9 499 911 290 ÷ 2 = 4 749 955 645 + 0;
  • 4 749 955 645 ÷ 2 = 2 374 977 822 + 1;
  • 2 374 977 822 ÷ 2 = 1 187 488 911 + 0;
  • 1 187 488 911 ÷ 2 = 593 744 455 + 1;
  • 593 744 455 ÷ 2 = 296 872 227 + 1;
  • 296 872 227 ÷ 2 = 148 436 113 + 1;
  • 148 436 113 ÷ 2 = 74 218 056 + 1;
  • 74 218 056 ÷ 2 = 37 109 028 + 0;
  • 37 109 028 ÷ 2 = 18 554 514 + 0;
  • 18 554 514 ÷ 2 = 9 277 257 + 0;
  • 9 277 257 ÷ 2 = 4 638 628 + 1;
  • 4 638 628 ÷ 2 = 2 319 314 + 0;
  • 2 319 314 ÷ 2 = 1 159 657 + 0;
  • 1 159 657 ÷ 2 = 579 828 + 1;
  • 579 828 ÷ 2 = 289 914 + 0;
  • 289 914 ÷ 2 = 144 957 + 0;
  • 144 957 ÷ 2 = 72 478 + 1;
  • 72 478 ÷ 2 = 36 239 + 0;
  • 36 239 ÷ 2 = 18 119 + 1;
  • 18 119 ÷ 2 = 9 059 + 1;
  • 9 059 ÷ 2 = 4 529 + 1;
  • 4 529 ÷ 2 = 2 264 + 1;
  • 2 264 ÷ 2 = 1 132 + 0;
  • 1 132 ÷ 2 = 566 + 0;
  • 566 ÷ 2 = 283 + 0;
  • 283 ÷ 2 = 141 + 1;
  • 141 ÷ 2 = 70 + 1;
  • 70 ÷ 2 = 35 + 0;
  • 35 ÷ 2 = 17 + 1;
  • 17 ÷ 2 = 8 + 1;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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.


155 646 546 578 786(10) = 1000 1101 1000 1111 0100 1001 0001 1110 1000 1101 0110 0010(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 48.

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; ...

The first bit (the leftmost) is reserved for the sign:

0 = positive integer number, 1 = negative integer number


The least number that is:

1) a power of 2

2) and is larger than the actual length, 48,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the 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:


Number 155 646 546 578 786(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

155 646 546 578 786(10) = 0000 0000 0000 0000 1000 1101 1000 1111 0100 1001 0001 1110 1000 1101 0110 0010

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

More operations on signed integer numbers:

» Signed integer number 155 646 546 578 785 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 155 646 546 578 787 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

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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