Exam 2

Question 1

Carry Lookahead Adder (CLA)

Answer 1

All carries are computed ahead

All sum bits are computed as soon as their carry-in’s are available

All first level generate (g) functions are computed simultaneously

All first level propagate (p) functions are computed simultaneously

Question 2

For an arbitrary bit position i the propagate function is equal to

Answer 2

x_i+y_i ←(OR)

Question 3

Assuming that the maximum number of inputs to a CMOS gate is 4, the propagation delay to generate C8 is

Answer 3

3 Gate delay : g_i and p_i
(one for g_i and p_i, and two for SOP)
1 Gate delay: [PT]
1 Gate delay: final OR-ing

C8= 5 delay gates
C16=6
C24=7
C32=8

Question 4

Below is the schematic diagram of a one-digit BCD adder. The additional 2-bit adder and Cout gate logic is necessary to

Answer 4

Detect when the sum is >9 and if true set the Cout=1

Question 5

For identically sized operands, floating-point number representation

Answer 5

Covers a larger umber range than fixed-point representation

Needs packing and unpacking

Question 6

Before subtracting two floating-point numbers, these have to be

Answer 6

Unpacked and their decimal points aligned

Question 7

A 2-to-1 mux can be used to implement an inverter if

Answer 7

The signal to be inverted is tied to the mux select input, input0 of the mux is tied to 1, and input1 of the mux is tied to 0

Question 8

A 2x2 crossbar

Answer 8

Has 2 inputs and 2 outputs

Can route any of the two inputs to any of the two outputs

Can route one input to one output while routing the other input to the other output

Is a key element of data network routers

Question 9

Below is the diagram of a 3-input LUT, as used in FPGAs. Following the same structure, a 4-input LUT uses

Answer 9

16 memory cells and 15 2-to-1 muxes

Question 10

If f= ~x1(x2+x3) + x1(x2x3), then

Answer 10

The function is expanded by x2

x2x3 is the f_x1 cofactor

x2+x3 is the f_`~x1 cofactor

Need at least a 2 to1 mux to implement it

Question 11

If we expand a 4-variable function in terms of 2 variables (multi-variable expansion), then we need at least

Answer 11

A 4to1 mux or

Question 12

In a 3-to-8 decoder without enable, how many outputs are active at any given point in time?

Answer 12

1

Question 13

A 4-to-16 decoder can be built using a decoder tree. How many 2-to-4 decoders with enable are necessary?

Answer 13

5

Question 14

The truth table of a priority encoder is shown below. Which is the correct priority order, starting with the highest priority?

Answer 14

X0→x1→x2→x3