Posted by **Francesca** on Thursday, September 8, 2011 at 7:05pm.

1.) Express each decimal number as an 8-bit binary number in the 2's complement form and then find the negative of the representation of that number in two’s compliment

a.) +18

b) -117

Thanks for any help!

- Computing in Security (Conversion Help) -
**MathMate**, Thursday, September 8, 2011 at 11:02pm
Two's complement is a notation that represents both positive and negative numbers. The most significant (left-most) is the sign bit, which is turned on when the number is negative.

Unlike the one's complement, there is only one representation of zero.

For an eight-bit number, the range goes from -128 to 127.

A positive number is represented by a usual binary number format, using the 7 low-order (right-most) bits, and represent from 0 to 127.

A negative number is simply the reversal of the bits and then add 1.

Example:

10(decimal)=00001010(binary)

-10(decimal)=11110101 + 1

=11110110

18(decimal)=00010010(binary)

-18(decimal)=11101101 + 1

=11101110

and so on.

To negate a negative number, subtract one and reverse the bits.

For example,

-18(decimal)=11101110

subtract 1

11101101

Reverse bits

00010010 (binary -18)

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