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# lecture3-post - BME 303 Lecture 3 Review Binary numbers...

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1 BME 303 Lecture 3 • Review: Binary numbers – Unsigned – Signed • Hexadecimal • ASCII Characters (Text) • Floating Point Formats

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2 Announcements • Revised Office Hours: – Tuesday, 12:30 – 1:30 pm (½ hour earlier) – Friday, 9 am – 11 am • Revised homework deadlines: – All assignments now due Tuesday before class (not Thursday); Therefore HW #1 due next Tuesday, February 1 – Assignments still given before 9 am Friday morning
3 Reminders • Follow schedule for reading: Should have • When e-mailing me ([email protected]), start subject line with “BME303:” – won’t be filtered as spam then • Temporary course website: http://chaos.ph.utexas.edu/~mgmoore/bme303/ – Course syllabus and course schedule – Slides for lectures 1-4 – HW #1

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4 Review • Problem: Represent information (data) in a form mutually comprehensible by human and machine. • Solution: – Digitize/encode everything: convert to a numeric form – Represent these numbers in binary digits – bits! – Bits map nicely to circuits: on and off
5 Binary Digits: Bits • Internally, computers represent everything (data, instructions, etc.) using patterns of binary values • All bits are created equal: You must know what the bits are representing to interpret them • A group of 8 bits is called a byte

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6 Weighted Positional Number Systems Decimal: 35 254 = 4·10 0 + 5·10 1 + 2·10 2 + 5·10 3 + 3·10 4 Binary: (1 0110) 2 = 0·2 0 + 1·2 1 + 1·2 2 + 0·2 3 + 1·2 4 = 0 + 2 + 4 + 0 + 16 = (22) 10 4 5 2 5 3 d 0 d 1 d 2 d 3 d 4 0 1 2 3 4 0 1 1 0 1 b 0 b 1 b 2 b 3 b 4 0 1 2 3 4
7 Conversion between Unsigned Binary and Decimal 0 1 1 0 1 0 1 b 0 b 1 b 2 b 3 b 4 b 5 b 6 0 1 2 3 4 5 6 Example: convert decimal 86 to an 8-bit unsigned integer. 86/2 = 43 remainder 0 43/2 = 21 remainder 1 21/2 = 10 remainder 1 10/2 = 5 remainder 0 5/2 = 2 remainder 1 2/2 = 1 remainder 0 1/2 = 0 remainder 1 Reached 0, stop.

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8 Integers: Overview • Signed Magnitude • One’s Complement • Two’s Complement • Unsigned 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 Positive integers represented in the same way Negative integers differ (significantly!) Two’s complement most common signed format: makes implementing addition simplest
Two’s Complement • Problems with signed magnitude and 1’s complement – two representations of zero (+0 and -0) – arithmetic circuits are complex • How to add two sign-magnitude numbers? Try 2 + (-3) • How to add to one’s complement numbers? Try 4 + (-3) • Two’s complement representation developed to make circuits easy for arithmetic. – Just do “normal” addition, ignoring carry out

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lecture3-post - BME 303 Lecture 3 Review Binary numbers...

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