Convert 1 100 010 110 111 028 to a Signed Binary (Base 2)

How to convert 1 100 010 110 111 028(10), a signed base 10 integer number? How to write it as a signed binary code in base 2

What are the required steps to convert base 10 integer
number 1 100 010 110 111 028 to signed binary code (in base 2)?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 100 010 110 111 028 ÷ 2 = 550 005 055 055 514 + 0;
  • 550 005 055 055 514 ÷ 2 = 275 002 527 527 757 + 0;
  • 275 002 527 527 757 ÷ 2 = 137 501 263 763 878 + 1;
  • 137 501 263 763 878 ÷ 2 = 68 750 631 881 939 + 0;
  • 68 750 631 881 939 ÷ 2 = 34 375 315 940 969 + 1;
  • 34 375 315 940 969 ÷ 2 = 17 187 657 970 484 + 1;
  • 17 187 657 970 484 ÷ 2 = 8 593 828 985 242 + 0;
  • 8 593 828 985 242 ÷ 2 = 4 296 914 492 621 + 0;
  • 4 296 914 492 621 ÷ 2 = 2 148 457 246 310 + 1;
  • 2 148 457 246 310 ÷ 2 = 1 074 228 623 155 + 0;
  • 1 074 228 623 155 ÷ 2 = 537 114 311 577 + 1;
  • 537 114 311 577 ÷ 2 = 268 557 155 788 + 1;
  • 268 557 155 788 ÷ 2 = 134 278 577 894 + 0;
  • 134 278 577 894 ÷ 2 = 67 139 288 947 + 0;
  • 67 139 288 947 ÷ 2 = 33 569 644 473 + 1;
  • 33 569 644 473 ÷ 2 = 16 784 822 236 + 1;
  • 16 784 822 236 ÷ 2 = 8 392 411 118 + 0;
  • 8 392 411 118 ÷ 2 = 4 196 205 559 + 0;
  • 4 196 205 559 ÷ 2 = 2 098 102 779 + 1;
  • 2 098 102 779 ÷ 2 = 1 049 051 389 + 1;
  • 1 049 051 389 ÷ 2 = 524 525 694 + 1;
  • 524 525 694 ÷ 2 = 262 262 847 + 0;
  • 262 262 847 ÷ 2 = 131 131 423 + 1;
  • 131 131 423 ÷ 2 = 65 565 711 + 1;
  • 65 565 711 ÷ 2 = 32 782 855 + 1;
  • 32 782 855 ÷ 2 = 16 391 427 + 1;
  • 16 391 427 ÷ 2 = 8 195 713 + 1;
  • 8 195 713 ÷ 2 = 4 097 856 + 1;
  • 4 097 856 ÷ 2 = 2 048 928 + 0;
  • 2 048 928 ÷ 2 = 1 024 464 + 0;
  • 1 024 464 ÷ 2 = 512 232 + 0;
  • 512 232 ÷ 2 = 256 116 + 0;
  • 256 116 ÷ 2 = 128 058 + 0;
  • 128 058 ÷ 2 = 64 029 + 0;
  • 64 029 ÷ 2 = 32 014 + 1;
  • 32 014 ÷ 2 = 16 007 + 0;
  • 16 007 ÷ 2 = 8 003 + 1;
  • 8 003 ÷ 2 = 4 001 + 1;
  • 4 001 ÷ 2 = 2 000 + 1;
  • 2 000 ÷ 2 = 1 000 + 0;
  • 1 000 ÷ 2 = 500 + 0;
  • 500 ÷ 2 = 250 + 0;
  • 250 ÷ 2 = 125 + 0;
  • 125 ÷ 2 = 62 + 1;
  • 62 ÷ 2 = 31 + 0;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.

1 100 010 110 111 028(10) = 11 1110 1000 0111 0100 0000 1111 1101 1100 1100 1101 0011 0100(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; ...
  • 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, 50,

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:


1 100 010 110 111 028(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 100 010 110 111 028(10) = 0000 0000 0000 0011 1110 1000 0111 0100 0000 1111 1101 1100 1100 1101 0011 0100

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

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How to convert signed base 10 integers in decimal 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