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Explain the operation of a full subtractor with necessary diagrams. What is the difference between half and full subtractor?


Consider the following register transfer statements for two 4-bit registers R1 and R2.
xT: R1← R1+ R2
x' T: R1 ← R2
Every time that variable T = 1, either the content of R2 is added to the content of Rl if
x = 1, or the content of R2 is transferred to R1 if x = 0. Draw a diagram showing the
hardware implementation of the two statements. Use block diagrams for the two 4-bit
registers, a 4-bit adder, and a quadruple 2-to-1-llne multiplexer that selects the inputs
to R l . In the diagram, show how the control variables x and T select the inputs of the
multiplexer and the load input of register R1.
A Boolean function fk of two variables A and B is defined as follows:
fk (0, 0) = fk (0, 1) = fk (1, 1) = 1; fk (1, 0) = 0
Assuming complements of A and B are not available, what will be the minimum cost
solution for realizing using only 2-input NOR gates and 2-input OR gates (each
having unit cost) ? Explain with nessessary digram and expression.

Domestic LPG cylinder has the following dimensions: height = 580 mm, diameter = 318 mm. Assume there is only butane in the cylinder. Given that the initial pressure inside the cylinder is 2.5 bar and the ambient temperature is 298.15 K. According to the print on the cylinder, a full cylinder has 15 kg gas. Some part of butane is in liquid state and some part is in gas state. Use Redlich Kwong equation of state for all process calculations. (a) Develop the expression for total moles of the gas in terms of volume of cylinder, molar volume of liquid butane, molar volume of gaseous butane, fraction of cylinder volume filled with liquid butane. [2] (b) Convert the above relationship in terms of liquid compressibility factor Zl and gas compressibility factor Zv [2] (c) Use the above relationship to develop the equation for finding the fraction of cylinder volume filled with liquid butane. [2] (d) Estimate Zl [10] (e) Estimate Zv [10] (f) Estimate fraction of cylinder volume filled with liquid butane. [5]


QUESTION 8 Given               B 2 31 2 21 1 32 find the eigenvalues of B and an eigenvector for B corresponding to  1. (10) [10] QUESTION 9 A function f(x) is defined by:      2 fx x x , Determine the Fourier expansion of the periodic function f(x) with period 2 . (12) [12]


A man borrowed P10,000 from a bank and agreed to pay the loan at the end of 10 months. The bank
discounted the loan and gave him P9,500 in cash.
a) What was the rate of discount?
b) What was the rate of interest?
c) What was the rate of interest for one year?
Mr. J de la Cruz borrowed money from a bank. He received from the bank P1,342 and promise to pay
P1,500 at the end of 9 months.
1. Determine the discount rate or often referred to as “Banker’s discount”
2. Determine the simple interest rate
a machine of mass 100 kg is supported on openings of total stiffness 800 kn/m and has a rotating unbalanced element which results in a disturbing force of 400 n at a speed of 3000 r.p.m. assum-ing the damping ratio as 0.25, determine : 1. the amplitude of vibrations due to unbalance ; and 2. the transmitted force.

An electrically driven road vehicle of mass 450kg has four wheels of effective diameter 400mm radius of gyration 125mm and mass 9kg. The armature of the electric motor has a mass of 65kg a radius of gyration of 100mm and rotates at 4 times the speed of the road wheels. The rolling resistance to motion of the vehicle is to be assumed constant at 225N. Determine the acceleration of the vehicle if it is allowed to run freely down a slope whose inclination to the horizontal is sin-¹ 0.2


Assume an isotropic antenna operating at 10 GHz, find the effective area and antenna gain.
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