Base ten decimal system signed integer number 5 432 695 converted to signed binary in two's complement representation

How to convert a signed integer in decimal system (in base 10):
5 432 695(10)
to a signed binary two's complement representation

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;
  • 5 432 695 ÷ 2 = 2 716 347 + 1;
  • 2 716 347 ÷ 2 = 1 358 173 + 1;
  • 1 358 173 ÷ 2 = 679 086 + 1;
  • 679 086 ÷ 2 = 339 543 + 0;
  • 339 543 ÷ 2 = 169 771 + 1;
  • 169 771 ÷ 2 = 84 885 + 1;
  • 84 885 ÷ 2 = 42 442 + 1;
  • 42 442 ÷ 2 = 21 221 + 0;
  • 21 221 ÷ 2 = 10 610 + 1;
  • 10 610 ÷ 2 = 5 305 + 0;
  • 5 305 ÷ 2 = 2 652 + 1;
  • 2 652 ÷ 2 = 1 326 + 0;
  • 1 326 ÷ 2 = 663 + 0;
  • 663 ÷ 2 = 331 + 1;
  • 331 ÷ 2 = 165 + 1;
  • 165 ÷ 2 = 82 + 1;
  • 82 ÷ 2 = 41 + 0;
  • 41 ÷ 2 = 20 + 1;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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:

5 432 695(10) = 101 0010 1110 0101 0111 0111(2)

3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 23.

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) indicates the sign,
1 = negative, 0 = positive.

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: 32.

4. Positive binary computer representation on 32 bits (4 Bytes) - if needed, add extra 0s in front (to the left) of the base 2 number, up to the required length:

5 432 695(10) = 0000 0000 0101 0010 1110 0101 0111 0111

Conclusion:

Number 5 432 695, a signed integer, converted from decimal system (base 10) to a signed binary two's complement representation:
5 432 695(10) = 0000 0000 0101 0010 1110 0101 0111 0111

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 two's complement representation

How to convert a base ten signed integer number to signed binary in two's complement representation:

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, switch all the bits on 0 to 1 and all the bits on 1 to 0 (reversing the digits).

5) Only if the initial number is negative, add 1 to the number at the previous point.

Latest signed integers converted from decimal system to binary two's complement representation

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