BME303: Introduction to Computing - Hexadecimal, Floating Point, and Boolean Algebra - Pro, Study notes of Biology

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BME303 Intro. to Computing Chapter 2 – cont’d

BME303 Intro. to Computing Hexadecimal? 0001001010101011 0001 0010 1010 1011 1 2 A^

B^2

1 12AB – a convenient way to represent binary strings

2 A^ B

BME303 Intro. to Computing

Hexadecimal Notation Working with long stringsof 1s and 0s is difficultWe use hexadecimal (or hex) notation asa form of shorthand11010110 = 0xD6 = # ???

1101 0110 = 0xD6 = # ??? Hex is a 16-base number systemHow to convert to/from hex? hint: use binary as middle-man What about sign?D^6 bbbbbbbb^7 6 5 4 3 2 1 01 1 0 1 0 1 1

BME303 Intro. to Computing Hexadecimal Numbers

Convert binary 0011011011010101 to hex 0x36D50011 0110 1101 0101^3 6 D^

5

Binary^ Hex^0000 00001 10010 20011 30100 40101

0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D^1110 E^1111 F^5

BME303 Intro. to Computing Floating Point

Computers represent real numbers using Floating Point notationsDecimal: 2007 = 2.007·

Binary: 100.11 = 1.0011·

S IEEE Standard : (−1)·1.fraction·

exponent−127^ (1^ ≤^ exponent^ ≤^ 254)

S exponent (8-bit)^ fraction (23-bit) 31 30 29 28 27 26 25 24 23 22 21

20 19 18 17 16 15 14 13 12 11 10

9 8 7 6 5 4 5 2 1 0

32 bits total; exponent is an unsigned 8-bit integer

BME303 Intro. to Computing Floating Point

S(−1)·1.fraction·2 Three step process:- convert the decimal number to a binary number- write binary number in “normalized” scientific notation- find the exponential term

IEEE Standard for Floating Point Arithmetic (“rules”)exponent−127^ (1^ ≤^ exponent^ ≤^ 254)

-^ find the exponential term - store the number in the proper formatS exponent (8-bit)^ fraction (23-bit) 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17

16 15 14 13 12 11 10 9 8 7 6

5 4 5 2 1 0

BME303 Intro. to Computing Floating Point: Example

• Exponent field is 00000000 - #0• Exponent field is 11111111 - #inf

BME303 Intro. to Computing Floating Point Notation

S exponent (8-bit)^ fraction (23-bit) 31 30 29 28 27 26 25 24 23 22 21

20 19 18 17 16 15 14 13 12 11 10

9 8 7 6 5 4 5 2 1 0

Conversion: Binary to decimal

Sexponent−127 (−1)·1.fraction·

(1^ ≤^ exponent^ ≤^ 254)

BME303 Intro. to Computing Floating Point Notation Conversion: Decimal to Binary 0 133−127^ (−1)·1.1011·2= +1101100 = 108

Sexponent−127^ (−1)·1.fraction·2(

≤^ exponent^ ≤^ 254)

S exponent (8-bit)^ fraction (23-bit) 31 30 29 28 27 26 25 24 23 22 21

20 19 18 17 16 15 14 13 12 11 10

9 8 7 6 5 4 5 2 1 0

-^ First convert to binary •^ Then convert to exp and fraction

BME303 Intro. to Computing Floating Point Notation Convert Decimal 0.625 to Binary Step 1 : .625 x 2 = 1.25, the first binary digit to the right of the point is a 1. Step 2 : .25 x 2 = 0.50, the second binary digit to the right of the point is a 0.

.25 x 2 =^0 .50, the second binary digit to the right of the point is a

Step 3 : .50 x 2 = 1.00, the third binary digit to the right of the point is a 1. Step 4 : We are finished in Step 3,because we had 0 as the fractional part of our result there.Hence the representation of .625 = .101 b.

BME303 Intro. to Computing Text: ASCII Characters

•American Standard Code for Information Interchange•ASCII: Maps 128 characters to 7-bit code.–^ both printable and non-printable (ESC, DEL, …) characters^00 nul^10 dle^20 sp

30 0 40 @^50 P^60

`^70 p 01 soh^11 dc1^21!^31

41 A^51 Q^61 a^71 q 02 stx^12 dc2^22 "^32

42 B^52 R^62 b^72 r 03 etx^13 dc3^23 #^33

43 C^53 S^63 c^73 s 04 eot^14 dc4^24 $^34

44 D^54 T^64 d^74 t 04 eot^14 dc4^24 $^34

44 D^54 T^64 d^74 t 05 enq^15 nak^25 %^35

45 E^55 U^65 e^75 u 06 ack^16 syn^26 &^36

46 F^56 V^66 f^76 v 07 bel^17 etb^27 '^37

47 G^57 W^67 g^77 w 08 bs^18 can^28 (^38

48 H^58 X^68 h^78 x 09 ht^19 em^29 )^39

49 I^59 Y^69 i^79 y 0a^ nl^ 1a^ sub^ 2a^ *^ 3a^ :^

4a^ J^ 5a^ Z^ 6a^ j^ 7a^ z 0b^ vt^ 1b^ esc^ 2b^ +^ 3b^ ;^

4b^ K^ 5b^ [^ 6b^ k^ 7b^ { 0c^ np^ 1c^ fs^ 2c^ ,^ 3c^ <^

4c^ L^ 5c^ ^ 6c^ l^ 7c^ | 0d^ cr^ 1d^ gs^ 2d^ -^ 3d^ =^

4d^ M^ 5d^ ]^ 6d^ m^ 7d^ } 0e^ so^ 1e^ rs^ 2e^.^ 3e^ >^

4e^ N^ 5e^ ^^ 6e^ n^ 7e^ ~ 0f^ si^ 1f^ us^ 2f^ /^ 3f^?^

4f^ O^ 5f^ _^ 6f^ o^ 7f^ del

BME303 Intro. to Computing Text: ASCII Characters ASCII Symbol Names NUL null SOH start of heading STX start of text ETX end of text EOT end of transmission

ENQ^ enquiry ACK^ acknowledge BEL^ bell BS^ backspace TAB^ horizontal tab NL^ new line (or LF, line feed) VT^ vertical tab

BME303 Intro. to Computing Boolean Algebra

•^ Boolean logic is a branch of mathematics that deals withrules for manipulating the two logical values: true

and false^23

•^ Named after George Boole (1815-1864), an Englishmathematician, who was first to develop and describe aformal system to work with truth values•^ Why is Boolean logic so relevant to computers?^ – direct mapping to binary digits– 1 = true, 0 = false– Devices for basic logical operations

BME303 Intro. to Computing Boolean Expression

-^ A Boolean expression is a condition•^ A Boolean expression is any expression that evaluates to eithertrue or false^ – Is the expression 1+3 a Boolean condition? •^ Examples of Boolean expressions:^ 5 > 3 (true, or 1) 5 > 3 (true, or 1) xA > x2X < YY = 20052003 > 2005 (false, or 0) • Bits may be interpreted as logical values (sometimes referred to as truth values ), where 1 means TRUE and 0 means FALSE