### Fast Fact: Root Mean Squared Unraveled

RMS or Root Mean Squared is defined as the Root of the Mean of the Square of each sampled value of a signal (for discrete values) or the Root of the Definite Integral of the Square of each bounded function (for continuous values). But what exactly does it mean? It is actually like a means of central tendency (I use the word "like" because it doesn't exactly function the same way as an average) only that negative integers are treated as positive values by squaring them in the first place. After squaring, you take the "mean" then take the square root again to reverse the effects of squaring. Thus, the entire signal is sufficiently represented by one constant value. This constant value can be taken as DC (direct current) since DC is a constant unchanging voltage. Hence, when we take an RMS measurement of an AC signal, we are actually getting an equivalent DC signal that can replace that AC signal in terms of power delivery.

But why not use Cube-Root Mean Cube or higher exponentials? Well, I've tried it in Matlab, and when you observe the change in the final value when you tweak the signal, you'll find that the sensitivity to change is highest when squared and gets worse when you "CMC" it or treat it with higher exponentials. For example, take the vector [10 20 12 15 7 9]. Its RMS, CMC, etc. is 14.6002, 15.2561, and 15.8017 respectively. When you try and tweak one component of the vector, say increase the first element by 3, yielding [13 20 12 15 7 9], the resulting RMS, CMC, etc. is 14.9889, 15.5366, and 15.9942. Now let us get the sensitivity of each:

RMS

14.9889-14.6002=0.3887

CMC (Cube-root Mean Cube)

15.5366-15.2561=0.2805

Etc. (actually raised each to the 4th , got the mean, and took the 4th root)

15.9942-15.8017=0.1925

It is directly observable that RMS yields optimum sensitivity to change. Also, CMC is disqualified from the beginning since it doesn't remove negative components at all.

(Note: I only made up the CMC term. I'm not sure whether such a term was really coined. Hahaha...)

### Calculator Techniques for the Casio FX-991ES and FX-991EX Unraveled

In solving engineering problems, one may not have the luxury of time. Most situations demand immediate results. The price of falling behind schedule is costly and demeaning to one's reputation. Therefore, every bit of precaution must be taken to expedite calculations. The following introduces methods to tackle these problems speedily using a Casio calculator FX-991ES and FX-991EX.

►For algebraic problems where you need to find the exact value of a dependent or independent variable, just use the CALC or [ES] Mode 5 functions or [EX] MENU A functions.

►For definite differentiation and integration problems, simply use the d/dx and integral operators in the COMP mode.

►For models that follow the differential equation: dP/dx=kt and models that follow a geometric function(i.e. A*B^x).

[ES]
-Simply go to Mode 3 (STAT) (5)      e^x
-For geometric functions Mode 3 (STAT) 6 A*B^x
-(Why? Because the solution to the D.E. dP/dx=kt is an exponential function e^x.
When we know the boundary con…

### Common Difficulties and Mishaps in 6.004 Computation Structures (by MITx)

Updated:
May 6, 2018
VLSI Project: The Beta Layout [help needed]Current Tasks: ►Complete 32-bit ALU layout [unpipelined] in a 3-metal-layer C5 process. ►Extend Excel VBA macro to generate code for sequential instructions (machine language to actual electrical signals).
Current Obstacles/Unresolved Decisions:
►Use of complementary CMOS or pass transistor logic (do both? time expensive, will depend on sched.
►Adder selection: Brent-Kung; Kogge Stone; Ladner Fischer (brent takes up most space but seems to be fastest, consider fan-out) [do all? time expensive, will depend on sched.)
►layout requirements and DRC errors