36. UNITS AND CONVERSIONS36.1 HOW TO USE UNITS36.2 HOW TO USE SI UNITS36.3 THE TABLE36.4 ASCII, HEX, BINARY CONVERSION36.5 G-CODESunits - 36.136. UNITS AND CONVERSIONS• Units are essential when describing real things.• Good engineering practice demands that each number should always be accom-panied with a unit.36.1 HOW TO USE UNITS• This table does not give an exhaustive list of conversion factors, but instead a minimal (but fairly complete) set is given. From the values below any conversion value can be derived. If you are not sure about this, ask the instructor to show you how.• A simple example of unit conversion is given below,dx10m= dy5ft·=Given,**a simple unit conversion example:Find the distance ‘d’,ddx2dy2+=d∴ 10m()25ft()2+=d∴ 100m225ft2+=1ft 0.3048m=1∴0.3048m1ft---------------------=d∴ 100m225ft20.3048m1ft---------------------2+=d∴ 100m225ft20.092903()m2ft2------+=d∴ 100m225 0.092903()m2+=d∴ 102.32m210.12m==From the tableskeep the units in the equationmultiply by 1cancel out unitsunits - 36.236.2 HOW TO USE SI UNITS1. Beware upper/lower case letter in many cases they can change meanings.e.g. m = milli, mega2. Try to move prefixes out of the denominator of the units.e.g., N/cm or KN/m3. Use a slash or exponents.e.g., (kg•m/s2) or (kg•m•s-2)4. Use a dot in compound units.e.g., N•m5. Use spaces to divide digits when there are more than 5 figures, commas are avoided because their use is equivalent to decimal points in some cultures.• In some cases units are non-standard. There are two major variations US units are marked with ‘US’ and Imperial units are marked with ‘IMP’.36.3 THE TABLEMajor DivisionDistance1 ft. (feet) = 12 in. (inches) = 0.3048 m (meter)1 mile = 1760 yards = 5280 ft = 1.609km1 in.(inch) = 2.540 cm1 yd (yard) = 3 ft.1 nautical mile = 6080 ft. = 1852 m = 1.150782 mi1 micron = 10-6 m1 angstrom = 10-10 m1 mil = 10-6 m1 acre = 43,560 ft. = 0.4047 hectaresunits - 36.31 furlong = 660 ft1 lightyear = 9.460528e15 m1 parsec = 3.085678e16 mArea1 acre = 43,559.66 ft21 Hectare (ha) = 10,000 m21 Hectare (ha) = 10,000 m21 Hectare (ha) = 10,000 m21 Hectare (ha) = 10,000 m2Velocity1 mph = 0.8689762 knotAngle1 rev = 2PI radians = 360 degrees = 400 gradians1 degree = 60 minutes1 minute = 60 secondsVolume1 US gallon = 231 in31 CC = 1 cm31 IMP gallon = 277.274 in31 barrel = 31 IMP gal. = 31.5 US gal.1 US gal. = 3.785 l = 4 quarts = 8 pints = 16 cups1 liter (l) = 0.001 m3 = 2.1 pints (pt) = 1.06 quarts (qt) = 0.26 gallons (gal)1 qt (quart) = 0.9464 l1 cup (c) = 0.2365882 l = 8 USoz1 US oz = 8 U.S. drams = 456.0129 drops = 480 US minim = 1.040842 IMP oz= 2 tablespoons = 6 teaspoons1 IMP gal. = 1.201 U.S. gal.1 US pint = 16 US oz1 IMP pint = 20 IMP oz1tablespoon = 0.5 oz.1 bushel = 32 quarts1 peck = 8 quartsForce/Mass1 N (newton) = 1 kg•m/s2 = 100,000 dyne1 dyne = 2.248*10-6 lb. (pound)1 kg = 9.81 N (on earth surface) = 2.2046 lb 1lb = 16 oz. (ounce) = 4.448Nunits - 36.41 oz. = 28.35 g (gram) = 0.2780N1 lb = 0.03108 slug1 kip = 1000 lb.1 slug = 14.59 kg1 imperial ton = 2000 lb = 907.2 kg1 metric tonne = 1000 kg1 troy oz = 480 grain (gr)1 g = 5 carat1 pennyweight = 24 grain1 stone = 14 lb1 long ton = 2240 lb1 short ton = 2000 lbPressure1 Pascal (Pa) = 1 N/m2 = 6.895 kPa1 atm (metric atmos.) =760 mmHg at 0°C=14.223 lb/in2=1.0132*105 N/m21 psi = 2.0355 in. Hg at 32F = 2.0416 in. Hg at 62F1 microbar = 0.1 N/m2Scale/Magnitudeatto (a) = 10-18femto (f) = 10-15pico (p) = 10-12nano (n) = 10-9micro (µ) = 10-6milli (m) = 10-3centi (c) 10-2deci (d) = 10-1deka (da) = 10hecto (H) = 102kilo (K) = 103mega (M) = 106giga (G) = 109tera (T) = 1012peta (P) = 1015exa (E) = 1018Power1 h.p. (horsepower) = 745.7 W (watts) = 2.545 BTU/hr. = 550 ft.lb./sec.1 ft•lb/s = 1.356 W1 J (joule) = 1 N•m = 107 ergs = 0.2389 cal.1 W = 1 J/sunits - 36.51 ev = 1.60219*10-19 J1 erg = 10-7 JTemperature°F = [(°C*9)/5]+32, °C = Celsius (Centigrade), F = FahrenheitK = KelvinRankine (R) = F - 459.6660.252 calories = 1 BTU (British Thermal Unit)-273.2 °C = -459.7 °F = 0 K = 0 R = absolute zero0 °C = 32 °F = 273.3 K = 491.7 R = Water Freezes100°C = 212°F = 373.3 K = 671.7 R = Water Boils (1 atm. pressure)1 therm = 100,000 BTUMathematicalπ radians = 3.1416 radians = 180 degrees = 0.5 cycles1 Hz = 1 cycle/sec.1 rpm (revolutions per minute) = 60 RPS (Revolutions per second) = 60Hz1 fps (foot per second) = 1 ft/sec1 mph (miles per hour) = 1 mi./hr.1 cfm (cubic foot per minute) = 1 ft3/min.e = 2.718Time1 Hz (hertz) = 1 s-11 year = 365 days = 52 weeks = 12 months1 leap year = 366 days1 day = 24 hours1 fortnight = 14 days1 hour = 60 min.1 min = 60 seconds1 millenium = 1000 years1 century = 100 years1 decade = 10 yearsPhysical ConstantsR = 1.987 cal/mole K = ideal gas law constantK = Boltzmann’s constant = 1.3x10-16 erg/K = 1.3x10-23 J/Kh = Planck’s constant = 6.62x10-27 erg-sec = 6.62x10-34 J.secAvagadro’s number = 6.02x1023 atoms/atomic weightdensity of water = 1 g/cm3electron charge = 1.60x10-19 coul.electron rest mass = 9.11*10**-31 kgproton rest mass = 1.67*10**-27 kgunits - 36.6speed of light (c) = 3.00x1010 cm/secspeed of sound in dry air 25 C = 331 m/sgravitational constant = 6.67*10**-11 Nm**2/kg**2permittivity of free space = 8.85*10**-12 farad/mpermeability of free space = 1.26*10**-6 henry/mmean radius of earth = 6370 Kmmass of earth = 5.98*10**24 kgElectromagneticmagnetic flux = weber (We) = 10**8 maxwellinductance = henrymagnetic flux density = tesla (T) = 10**4 gaussmagnetic intensity = ampere/m = 0.004*PI oerstedelectric flux density = coulomb/m**2capacitance = faradpermeability = henry/melectric field strength = V/mluminous flux = lumenluminance = candela/m**21 flame = 4 foot candles = 43.05564 lux = 43.05564 meter-candlesillumination = luxresistance = ohm36.4 ASCII, HEX, BINARY CONVERSION• The table below will allow conversions between decimal, binary, hexadecimal, and ASCII values. The values shown only go up to 127. ASCII values above this are not commonly used in robust applications.units -