CS 2700 - Mid-Term Cheat Sheet

Sign Magnitude:
+18 = 00010010
-18 = 10010010

Benefits: Simple
Drawbacks: addition and subtra­ction need to take sign and number into consid­eration for calcul­ations and there are two ways to represent 0.
To extend range: Move sign bit to new leftmost bit and fill rest with 0s

Two's Comple­ment:
Similar to sign magnitude, except for how the other digits except the signed one are consid­ered.
to extend range: move sign bit to new leftmost bit and fill rest with same sign as sign bit

Biased Repres­ent­ation
A fixed value is subtracted from the field

First generation computers: ENIAC -> IAS Computer -> UNIVAC
"von Neumann Machin­es"
Why important? - Stored­-Pr­ogram Concept
How does it work? - 1000 memory locations called words, which are 40 bits each. Each word is divided into a left and right instru­ction. Each instru­ction is divided into an 8 bit opcode saying the operation to be performed and a 12 bit address pointing to one of the words in memory. Repeatedly performs instru­ction cycles, divided between the fetch and execute cycles. In the fetch cycle, the opcode of the next instru­ction is loaded into the IR and the address portion is loaded into the MAR. This instru­ction may be taken from the IBR, or it can be obtained from memory by loading a word into the MBR and then down to the IBR, IR, and MAR. Once opcode is in IR, execute cycle is performed - opcode is interp­reted and sends out the approp­riate signals to cause data to be moved or an operation to be performed by the ALU

Second Genera­tion: Transi­stors
Transi­stors are smaller and cheaper than vacuum tubes. This created a huge boom in availa­bility of computers.

Third Genera­tion: Integrated Circuits
All of these components can now be produced in silicon chips instead of discrete compon­ents, further reducing the cost and size of computers.

The number of transi­stors that can be placed onto a chip doubles every year. revised to every 18 months since the 1970s

Import­ance:
1) Cost remains relatively the same while computing power doubles
2) Operating Speed is increased due to shorter electrical pathways because everything is so close together
3) Smaller size means computers can be placed in more enviro­nments
4) Reduction in power and cooling requir­ements
5) With more circuitry on each chip, there are fewer interchip connec­tions

CPI = (SUM_i=1<sup>n (CPI_i x I_i)) / I_C

T = I_C x CPI x Tau

Tau = 1/f

MIPS rate = I_C / (T x 10</sup>6 ^{) or f / (CPI x 10}6<sup>)

MFLOPS rate = (number of executed floati­ng-­point operations in a program) / (execution time x 10</sup>6^)

speedup (Amdah­l's Law) = 1 / ((1 - f) + (f/N))