Question

Question 1

i) A binary system uses 8-bits to represent an analog value ranging from 120 ounces to 700 ounces, determine the resolution of the system and interprete your result.

ii) Determine the number of bits that would be needed for the above resolution to improve to better than 0.01 ounces per increment. Interpret your results.

iii) Use the binary coded decimal (BCD) representation of integers to represent each of the following integers.

2194

4576

7865

3947

3782

Answer 1

Question 1:

(i) We know, resolution of the system = analog range / (2ⁿ - 1)

Number of bits used by the system = n = 8

The range of the analog value varies from 120 to 700 ounces

So, we have:

Resolution of the system = (700 - 120) / (2⁸ - 1)

or, Resolution of the system = 580 / (256 - 1)

or, Resolution of the system = 580 / 255

or, Resolution of the system = 2.274 units

(ii) Total increment = (700 - 120) ounces = 580 ounces

0.01 percent increment will add = (580 * 0.01) ounces = 5.8 ounces/inch (approximately)

So, the new resolution will be = (5.8 + 2.274) = 8.074

Let us consider, the number of bits = n

Resolution of the system = (700 - 120) / (2ⁿ - 1)

or, 8.074 = (700 - 120) / (2ⁿ - 1)

or, 8.074 = 580 / (2ⁿ - 1)

or, (8.074 * 2ⁿ) = 580 + 8.074

or, (8.074 * 2ⁿ) = 588.074

or, 2ⁿ = 72.83

or, n = 7 (as the ceil function is considered)

So, we can say that the number of bits required will be 7.

(iii) The decimal to Binary Coded Decimal (BCD) representation is shown below:

Decimal	Binary Coded Decimal (BCD)
2194	0010 0001 1001 0100
4576	0100 0101 0111 0110
7865	0111 1000 0110 0101
3947	0011 1001 0100 0111
3782	0011 0111 1000 0010

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