Convert 111 000 101 001 496 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 111 000 101 001 496(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
111 000 101 001 496 to a signed binary in two's (2's) complement representation?

  • 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.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 111 000 101 001 496 ÷ 2 = 55 500 050 500 748 + 0;
  • 55 500 050 500 748 ÷ 2 = 27 750 025 250 374 + 0;
  • 27 750 025 250 374 ÷ 2 = 13 875 012 625 187 + 0;
  • 13 875 012 625 187 ÷ 2 = 6 937 506 312 593 + 1;
  • 6 937 506 312 593 ÷ 2 = 3 468 753 156 296 + 1;
  • 3 468 753 156 296 ÷ 2 = 1 734 376 578 148 + 0;
  • 1 734 376 578 148 ÷ 2 = 867 188 289 074 + 0;
  • 867 188 289 074 ÷ 2 = 433 594 144 537 + 0;
  • 433 594 144 537 ÷ 2 = 216 797 072 268 + 1;
  • 216 797 072 268 ÷ 2 = 108 398 536 134 + 0;
  • 108 398 536 134 ÷ 2 = 54 199 268 067 + 0;
  • 54 199 268 067 ÷ 2 = 27 099 634 033 + 1;
  • 27 099 634 033 ÷ 2 = 13 549 817 016 + 1;
  • 13 549 817 016 ÷ 2 = 6 774 908 508 + 0;
  • 6 774 908 508 ÷ 2 = 3 387 454 254 + 0;
  • 3 387 454 254 ÷ 2 = 1 693 727 127 + 0;
  • 1 693 727 127 ÷ 2 = 846 863 563 + 1;
  • 846 863 563 ÷ 2 = 423 431 781 + 1;
  • 423 431 781 ÷ 2 = 211 715 890 + 1;
  • 211 715 890 ÷ 2 = 105 857 945 + 0;
  • 105 857 945 ÷ 2 = 52 928 972 + 1;
  • 52 928 972 ÷ 2 = 26 464 486 + 0;
  • 26 464 486 ÷ 2 = 13 232 243 + 0;
  • 13 232 243 ÷ 2 = 6 616 121 + 1;
  • 6 616 121 ÷ 2 = 3 308 060 + 1;
  • 3 308 060 ÷ 2 = 1 654 030 + 0;
  • 1 654 030 ÷ 2 = 827 015 + 0;
  • 827 015 ÷ 2 = 413 507 + 1;
  • 413 507 ÷ 2 = 206 753 + 1;
  • 206 753 ÷ 2 = 103 376 + 1;
  • 103 376 ÷ 2 = 51 688 + 0;
  • 51 688 ÷ 2 = 25 844 + 0;
  • 25 844 ÷ 2 = 12 922 + 0;
  • 12 922 ÷ 2 = 6 461 + 0;
  • 6 461 ÷ 2 = 3 230 + 1;
  • 3 230 ÷ 2 = 1 615 + 0;
  • 1 615 ÷ 2 = 807 + 1;
  • 807 ÷ 2 = 403 + 1;
  • 403 ÷ 2 = 201 + 1;
  • 201 ÷ 2 = 100 + 1;
  • 100 ÷ 2 = 50 + 0;
  • 50 ÷ 2 = 25 + 0;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 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.

111 000 101 001 496(10) = 110 0100 1111 0100 0011 1001 1001 0111 0001 1001 0001 1000(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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) indicates 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, 47,

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.


Decimal Number 111 000 101 001 496(10) converted to signed binary in two's complement representation:

111 000 101 001 496(10) = 0000 0000 0000 0000 0110 0100 1111 0100 0011 1001 1001 0111 0001 1001 0001 1000

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

Share

» More ops: Convert decimal 111 000 101 001 470 to signed binary in two's (2's) complement representation

» Calculations Performed by Our Visitors: Decimal Numbers Converted to Signed Binary in Two's (2's) Complement Representation. Data organized on a Monthly Basis

» Month 11, 2025 [November]: Decimal Numbers Converted to Signed Binary in Two's (2's) Complement Representation. Calculations performed during the month of: November - by our visitors

How to convert signed integers from decimal system to signed binary in two's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in two'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, keeping track of each remainder, until 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 must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will 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 1s and all 1 bits with 0s (reversing the digits).
  • 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

  • 1. Start with the positive version of the number: |-60| = 60
  • 2. Divide repeatedly 60 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 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:
    60(10) = 11 1100(2)
  • 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
    60(10) = 0011 1100(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
    !(0011 1100) = 1100 0011
  • 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
    -60(10) = 1100 0011 + 1 = 1100 0100
  • Number -60(10), signed integer, converted from decimal system (base 10) to signed binary two's complement representation = 1100 0100