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BME303_lecture3_chap2

# BME303_lecture3_chap2 - BME303 Intro to Computing Chapter 2...

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1 BME303 Intro. to Computing Chapter 2 Bits, Data Types, and Operations BME303 Intro. to Computing 2 Outline • Analog vs. Digital •B i t • Numbering systems • Data types

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2 BME303 Intro. to Computing 3 Analog vs. Digital Modern computers are digital devices V(t) time V(t) time Analog Digital v H (t) v L (t) BME303 Intro. to Computing 4 Bit (binary digit) A single “light bulb” can represent 2 states (0&1 or on&off) V(t) time v H (t)=2.9 v L (t)=0 1 – presence of a voltage 0 – no voltage present
3 BME303 Intro. to Computing Binary Numbers • A collection of “light bulb” can represent a series of those two states. – e.g. 8 light bulb can represent the following 8 bit numbers: • 0100 1101 • 1110 0101 • Computers use electronic (instead of light bulbs) to represent 0 & 1 and the binary numbering system 5 BME303 Intro. to Computing 6 Numbering systems Binary (0 and 1, also known as “base two”, uses two digits) Decimal (arabic, 0,1,2,3,4,5,6,7,8,9, uses ten digits) Hexadecimal (0,1,…,8,9,A,B,C,D,E,F, uses sixteen digits) The highest digit in base N is N-1 the highest single digit in base ten is ____ the highest single digit in base two is _____ the highest single “digit” in hexadecimal system is ____ In all number systems ______ is the first digit

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4 BME303 Intro. to Computing 7 Numbering Systems Decimal Hex (Hexadecimal) Binary 0 1 2 3 4 5 6 7 8 9 • Decimal – base 10 • Hex – base 16 • Binary – base 2 BME303 Intro. to Computing 8 Numbering Systems Decimal Hex (Hexadecimal) Binary 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 • Decimal – base 10 • Hex – base 16 • Binary – base 2
5 BME303 Intro. to Computing 9 Numbering Systems Decimal Hex (Hexadecimal) Binary 00 11 22 33 44 55 66 77 88 99 10 12 13 14 15 16 • Decimal – base 10 • Hex – base 16 • Binary – base 2 BME303 Intro. to Computing 10 Numbering Systems Decimal Hex (Hexadecimal) Binary 10 A B 12 C 13 D 14 E 15 F 16 • Decimal – base 10 • Hex – base 16 • Binary – base 2

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6 BME303 Intro. to Computing 11 Numbering Systems Decimal Hex (Hexadecimal) Binary 00 0 1 22 33 44 55 66 77 88 99 10 A B 12 C 13 D 14 E 15 F 16 • Decimal – base 10 • Hex – base 16 • Binary – base 2 BME303 Intro. to Computing • What about a base “N” numbering system? –N=7 12
7 BME303 Intro. to Computing 13 329 10 2 10 1 10 0 101 2 2 2 1 2 0 3 x100 + 2 x10 + 9 x1 = 329 1x4 + 0x2 + 1x1 = 5 most significant least significant Weighted positional notation Decimal Binary BME303 Intro. to Computing Weighted Positional Notation • Each position represent a power of N: – Decimal: 303 = __* 10 2 + __ *10 1 + __ *10 0 – Binary: 101b = __ * 2 2 + __ *2 1 + __ *2 0 . – Base N: xyz = x * N 2 + y * N 1 + z *N 0 14

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8 BME303 Intro. to Computing 15 Numbering Systems • How do you represent decimal number 13 or 3,453?
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BME303_lecture3_chap2 - BME303 Intro to Computing Chapter 2...

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