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Name and explain the main components of a von Neumann computer.
 Central Processing Unit:
 Consists of a control unit, ALU, registers and PC
 Mainmemory system:
 For program instruction and data storage
 I/O system:
 For input and output
Single data path between main memory and control unit of CPU for data and instruction transfer

How many megabytes (MB) are in 2 terabytes (TB)? Show your work. Hint: use powers of 2.
(2 terabytes )(2^{40} bytes/terabyte)(megabyte/2^{20} bytes )= 2^{21} megabytes

Is it possible for both Moore's Law and Rock's Law to continue to hold indefinitely? Explain your answer.
No
The current version of Moore's Law is usually conveyed as: "the density of silicon chips doubles every 18 months."
Rock's Law states: "The cost of capital equipment to build semiconductors will double every four years."
At this rate, by the year 2035, not only will the size of a memory element be smaller than an atom, but it would also require the entire wealth of the world to build a single chip.

Convert 39.8125_{10} to base 4 using any method discussed in class. Show all work
 39 / 4 = 9 R = 3
 9 / 4 = 2 R = 1
 2 / 4 = 0 R = 2
 0.8125 x 4 = 3.2500
 0.2500 x 4 = 1.0000
 39.8125_{10} = 213.31_{4}

Assuming two's complement 8bit representation, consider the following:
0 1 1 0 0 1 1 0
+ 0 1 1 1 0 1 1 0
1 1 0 1 1 1 0 0
Is the result correct (i.e., does the resulting number accurately represent the sum of the two values which are being added together)? Justify your answer.
The computation is carried out correctly, but the result is incorrect since carryin to the sign bit is not equal to carryout. Overflow has occurred.

Show how 0.28564453125_{10} = .01001001001_{2} would be stored using IEEE754 single precision (be sure to indicate the sign bit, the exponent, and the signicand elds).
0.28564453125_{10} = .01001001001_{2} = 1.001001001_{2} x 2^{2
} Sign = 1
 Exponent = 2 + 127 = 125_{10} = 01111101_{2}
 Significand = 001001001000000000000000
The result: 1 01111101 001001001000000000000000

Assume we are using 8bit two's complement representation. Use arithmetic shifting to multiply the value 00010100 by 4.

How many inputs does a decoder have if it has 128 outputs?
128 = 2^{7}_{ }= 7

Identify whether each of the following is based on combinational logic or sequential logic
(a) [2 points] D flipflop
(b) [2 points] Fulladder
(c) [2 points] Multiplexer
(d) [2 points] Memory
(e) [2 points] A digital circuit to implement F(x, y, z) = ~x~y + x * (y + ~z)
 a) Sequential
 b) Combinational
 c) Combinational
 d) Sequential
 e) Combinational

Consider the following characteristic table for a TM flipflop:
T  M  Q(t + 1)
0  0  0
0  1  Q(t)
1  0  ~Q(t)
1  1  Q(t)
We wish to show that a JK flipflop can be converted to an TM flipflop by adding gate(s) and inverter(s).
(a) [10 points] Construct a truth table which shows the required values of J and K for each possible T and M combination.
(b) [10 points] Write a Boolean expression in sumofproducts form for J. Write a Boolean expression in sumofproducts form for K.
(c) Draw the resulting circuit using only NAND gates and one JK flipflop.If you choose to simplify the function for J or K you must justify your simplification.(For partial credit you may implement the resulting circuit using one JK flipflop and any gate discussed in lecture.)
 a)
 T  M  Q(t + 1)  J  K
 0  0  0  0  1
 0  1  Q(t)  0  0
 1  0  ~Q(t)  1  1
 1  1  Q(t)  0  0
b)
 J = T * ~M
 K = ~T* ~M + T ~M
 c)
 Simplification of the expression for K:
 K = ~T ~M + T ~M
 = ~M (~T + T) > Distributivity
 = ~M (1) B > Complement
 = ~M > Identity
 Final circuit not drawn

