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0114-notes

# 0114-notes - CPSC 121 Lecture 5 Menu Topics Representing...

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Unformatted text preview: CPSC 121 Lecture 5 January 14, 2009 Menu January 14, 2009 Topics: Representing Values (contd) Example: 7 Segment LED Display Reading: Today: Epp 1.5 Friday: Epp 1.3 Next week: Epp 2.1, 2.3 Reminders: On-line Quiz 4 deadline 9:00pm January 15 READ the WebCT Vista course announcements board WebCT Vista: http://www.vista.ubc.ca www: http://www.ugrad.cs.ubc.ca/~cs121/ We now consider how we do simple arithmetic (addition/subtraction) with fixed width binary representations. Integer Arithmetic: Addition Lets add two bytes, both in octal and in binary: octal binary 263 10110011 120 01010000----------------------- 403 100000011 Positional notation, in any base, facilitates addition. One must take carry into account. In octal, when two columns sum to 8 (or more) carry to the left occurs. In binary, when two columns sum to 2 (or more) carry to the left occurs N=8: Overflow Occurs In the previous example, the sum requires 9 bits to specify. What if there only are the 8 bits in a byte to hold the result? One must be aware that in finite precision integer arithmetic, carry to the left of the leftmost bit is lost Thus, in 8 bit byte arithmetic, (with leading zeroes omitted): octal binary 263 10110011 120 01010000----------------------- 3 11 Representing Negative Numbers Want -n to be the number which when added to n gives 0 Consider the byte 179 10 = 263 8 = 10110011 2 decimal octal binary 179 263 10110011 76 114 01001100 1s complement of 179 77 115 01001101 2s complement of 179------------------------------------------------- 256 400 100000000 sum of lines 1 and 3 In n bit arithmetic, the sum of an n bit binary number and its 2s complement is zero. We represent a negative number by its 2s complement. We subtract m from n by adding n and -m. That is, n - m = n + (-m) 2s Complement Most modern digital computers use 2s complement binary arithmetic for integer addition/subtraction. By convention,Most modern digital computers use 2s complement binary arithmetic for integer addition/subtraction....
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0114-notes - CPSC 121 Lecture 5 Menu Topics Representing...

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