Converter to binary one's complement: converting decimal system (base ten) signed integer numbers

Convert decimal system (base ten) signed integer numbers to binary one's complement representation

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

-127 = 1000 0000Jan 18 09:31 UTC (GMT)
1,100 = 0000 0100 0100 1100Jan 18 09:31 UTC (GMT)
83 = 0101 0011Jan 18 09:31 UTC (GMT)
0 = 00Jan 18 09:31 UTC (GMT)
-16 = 1110 1111Jan 18 09:31 UTC (GMT)
35 = 0010 0011Jan 18 09:31 UTC (GMT)
478 = 0000 0001 1101 1110Jan 18 09:31 UTC (GMT)
-61 = 1100 0010Jan 18 09:31 UTC (GMT)
10 = 0000 1010Jan 18 09:31 UTC (GMT)
-65 = 1011 1110Jan 18 09:31 UTC (GMT)
140 = 0000 0000 1000 1100Jan 18 09:31 UTC (GMT)
-25 = 1110 0110Jan 18 09:31 UTC (GMT)
-9 = 1111 0110Jan 18 09:31 UTC (GMT)

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

Follow the steps below to convert a signed base 10 integer number to binary one's complement:

  • 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 that is to be converted to binary, keeping track of each remainder. STOP when the last quotient of the operations 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 to have 4, 8, 16, 32, 64, ... bit length (power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number obtained above, up to the right length, under these circumstances:
    a) if the length of the base 2 number is different of a power of 2 and/or
    b) if the first bit of the base 2 number is '1';
    This way the first bit (leftmost) will always be '0', correctly representing a positive number.
  • 5. To get the negative integer number representation in binary one's complement, replace all '0' bits with '1' and all '1' bits with '0'.

Example: convert negative number -49 from decimal system (base ten) to binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
  • iteration division quotient remainder
    1 49 : 2 = 24 1
    2 24 : 2 = 12 0
    3 12 : 2 = 6 0
    4 6 : 2 = 3 0
    5 3 : 2 = 1 1
    6 1 : 2 = 0 1
    Last quotient is ZERO => FULL STOP
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
    49(10) = 11 0001(2)
  • 4. Length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take 8 bits (the least power of 2 higher than 6) - add '0' in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in binary one's complement, replace all '0' bits with '1' and all '1' bits with '0':
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from decimal system (base 10) to binary one's complement representation = 1100 1110