Question

Show decimal values below in two complement binary notation with 6 bits.

a) 18

b) -12

Answer 1

a) 18

• A positive number is the same in unsigned form and also in two's complement form.
• To find the two's complement form of a positive number, just represent the decimal integer in its binary form
• Convert 18 to binary
  • 18/2 9 - 0
  • 9/2 4 - 1
  • 4/2 2 - 0
  • 2/2 1 - 0
• The binary equivalent of 18 is 10010 and when it represented in 6 bits, it is 010010
• Two's complement of 18 is same as the positive notation.
• Answer is 010010₂

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b) -12

• To find the two's complement form of a negative number, first represent the decimal integer in its binary form
• Invert all the bits in the binary ,which means convert 1's to 0's and 0's to 1's
• Add 1 to the Inverted answer
• The resultant binary number is the two's complement representation of the decimal integer.
• Convert 12 to binary
  • 12/2 6 - 0
  • 6/2 3 - 0
  • 3/2 1 - 1
  • 1/2 0 - 1
• The binary equivalent of 12 is 01100 and when it represented in 6 bits, it is 001100
• Invert the bits and the result is 110011
• Add 1 to this result. 110011+1 => 110100
• Two's complement of -12 is 110100
• Answer is 110100₂

_{Below diagram shows the addition of 110011 and 1}

_{The first row specifies the carry and the last row specifies the sum.}

_{1+1 = sum (0) carry (1)}

_{0+1 = sum(1) carry (0)}

_{1+0 = sum(1) carry (0)}

_{0+0 = sum(0) carry(0)}

			1	1
1	1	0	0	1	1	+
					1	=
1	1	0	1	0	0	sum