{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

8.28 Binary & Representation Of Numbers

# Signmagnitudeuseanextrabitfor 51010101 51011101

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: atch?v=GcDshWmhF4A Binary Subtraction Decimal Subtraction Binary Subtraction 8423 6915 ­­­­­­­­­­ 1101011 1001101 ­­­­­­­­­­­ ..wait.. What about 1001101 – 1101011? How do we represent negative numbers? Properties of a Properties of a Good Representation Should be simple Allows us to do useful things Should be efficient Recovering from errors should be possible Negative Numbers Negative Numbers How would we represent ­5 in binary? Sign­magnitude: use an extra bit for +/­ + 5 = (+) 101 = 0101 ­ 5 = (­) 101 = 1101 (this assumes we have a fixed (known) word size so that we know the first bit represents +/­, and not the next power of 2) What about 0? – different 0’s can cause problems Negative Numbers Negative Numbers Sign­magnitude (use one bit for sign) is perfectly acceptable, with minor inconvenience, but is not as good as a clever alternative. “Two’s complement notation” is used. – – – only one representation of 0 allows computation of subtraction via addition a bit confusing on first sight. Towards understanding two’s complement: Towards understanding two Using 1 digit Suppose we had the symbols 0 through 9. How many (positive and negative) numbers can we represent? Which symbol gets which number? 10’s complement 10 0 ­1 ­2 ­3 9 8 0 1 1 7 ­4 3 5 ­5 4 2 2 repr...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online