Engineering Output Engineering Notation Similar to scientific notation

Engineering Output Engineering Notation: • Similar to scientific notation. • Exponent is evenly divisible by 3 • 1 <= mantissa < 1000 • The x 10 n portion is replaced by a “units prefix” Examples: • 3495 V -> 3. 495 k. V • 0. 00008763 A -> 87. 63 u. A

Engineering Output Function int Put. V_Eng(double v, int sigfigs, char *units) v : Value to be output sigfigs : number of sig figs to display units : string containing the units name to append. RETURNS: Number of characters printed.

SI Standard Prefixes Scale 103 106 109 Prefix k kilo M Mega G Giga Scale 10 -3 10 -6 10 -9 1012 1015 1018 1021 1024 T P E Z Y 10 -12 10 -15 10 -18 10 -21 10 -24 Tera Peta Exa Zetta Yotta Prefix m milli u micro n nano p pico f femto a atto z zepto y yocto

Significant Figures Measure of the accuracy and/or precision of a value. • Values are assumed known to +/- 0. 5 sig fig. • Determines how many digits are reported. • By convention, a leading 1 is not considered significant. • By convention, trailing zeroes not considered significant. Examples: • 3. 495 k. V has 4 sig figs. • 17. 63 u. A has 3 sig figs. • 400 m has 1 sig fig. (unless told otherwise).

Rounding Round to nearest least significant digit. • Visually, we look to see if the next digit is 5 or greater. • Our output algorithm automatically truncates (ignores) any digits to the right of the last digit output. • Algorithmically, we can simply add 0. 5 sig fig and truncate. Examples: • 4. 53243 rounds to 4. 532 with 4 sig. figs. • 4. 53243 + 0. 0005 = 4. 532 | 93 (only output 4 digits) • 2. 38954 rounds to 2. 39 with 3 sig figs. • 2. 38954 + 0. 005 = 2. 39 | 454 (only output 3 digits)

Rounding Normalized Values In scientific notation, the value v can be expressed using a mantissa (m) and an exponent (e) as follows: v = m x 10 e This value is normalized if m has exactly one non-zero digit to the left of the decimal point, i. e, if: 1. 0 <= m < 10. 0 Ignoring significant of leading 1 (for now), 0. 5 sig fig is then: hsf = 5 x 10 -N (hsf - “hemi-sig fig) If m has a leading 1, then hsf is another factor of ten smaller: hsf = 0. 5 x 10 -N

Top Level Decomposition 1) TASK: Output negative sign and take absolute value. 2) TASK: Determine the mantissa and the exponent. 3) TASK: Add 0. 5 Sig Fig to Mantissa 4) TASK: Scale mantissa so that exponent is divisible by 3. 5) TASK: Output mantissa to N sig figs. 6) TASK: Output prefix based on exponent. 7) TASK: Output units. 8) TASK: Return number of characters printed.

Hand Example v = -0. 00001846774 to 4 sig figs 1) TASK: Output negative sign and take absolute value. OUTPUT: ‘-’ v = 0. 00001846774 2) TASK: Determine the mantissa and the exponent. m = 1. 846774 e = -5 3) TASK: Add 0. 5 Sig Fig to Mantissa hsf = 5 x 10 -4 = 0. 0005 hsf = hsf/10 = 0. 00005 (since m < 2) m = m + hsf = 1. 846774 + 0. 00005 = 1. 846824

Hand Example (cont’d) 4) TASK: Scale mantissa so that exponent is divisible by 3. e = -4 not divisible by 3. Multiply mantissa by 10 and decrement exponent until it is. m = 18. 46824 e = -3 5) TASK: Output mantissa to N sig figs. Output m to (N+1 digits since leading digit was a 1) OUTPUT: 18. 468 6) TASK: Output prefix based on exponent. OUTPUT: m 7) TASK: Output units.

Put. V_Eng() Task 1 int Put. V_Eng(double v, int sigfigs, char *units) { int i, c, e; double m, hsf; /* if { TASK (n < 1 - Handle negative values */ 0. 0) Put. C(‘-’); return 1 + Put. V_Eng(-v, sigfigs, units); }

Put. V_Eng() Task 2 /* TASK 2 - Determine mantissa and exponent */ m = 0. 0; e = 0; if (v != 0. 0) { while (v >= 10. 0) { v /= 10. 0; e++; } while (v < 1. 0) { v *= 10. 0; e--; } }

Put. V_Eng() Task 3 /* TASK 3 - Add 0. 5 sig fig */ hsf = (m < 2. 0)? 0. 5 : 5. 0; for (i = 0; i < sigfigs; i++) hsf /= 10. 0;

Put. V_Eng() Task 4 /* TASK 4 - Make exponent divisible by 3 */ while (e%3) { m *= 10. 0; e--; }

Put. V_Eng() Task 5 /* TASK 5 - Output Mantissa */ c = Put. V_lf. N(m, sigfigs + ((m<2. 0)? 1 : 0) ); /* The Put. V_lf. N() function is basically the Put. V_lf() function except that it only puts out N digits (followed by trailing zeros if necessary). */

Put. V_Eng() Task 6 /* TASK 6 - Output Prefix */ switch(e) { case -24: Put. C(‘y’); c++; break; case -21: Put. C(‘z’); c++; break; /*. . . */ case -3: Put. C(‘m’); c++; break; case 0: break; case 3: Put. C(‘k’); c++; break; /*. . . */ case 21: Put. C(‘Z’); c++; break; case 24: Put. C(‘Y’); c++; break; default: Put. C(‘e’); c += 1 + Put. V_i(e); }

Put. V_Eng() Task 7 / 8 /* TASK 7 - Output Units */ c += Put. S(units); /* TASK 8 - Return number of characters */ return c; }