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Phrases Data Representation - Number System PYQ



If we can generate a maximum of 4 Boolean functions using n Boolean variables, what will be minimum value of n?

NIMCET PREVIOUS YEAR QUESTION 





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Solution

Question: If we can generate a maximum of 4 Boolean functions using n Boolean variables, what is the minimum value of n?

Formula: Number of Boolean functions of n variables is:

22n

Condition: We are told the total functions must be ≤ 4:

22n4

✅ Try values of n:

  • n=0: 220=21=2
  • n=1: 221=22=4
  • n=2: 222=24=16

Minimum n for which number of Boolean functions ≤ 4 is:

1

✅ Final Answer: 1



The representation of a floating point binary number +1001.11 in 8 bit fraction and 6 bit exponent format is





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Solution

✅ Given:

The floating-point binary number is +1001.112.

We need to convert it into an 8-bit fraction and a 6-bit exponent format.

✅ Step 1: Normalize the Binary Number

We start by normalizing the binary number into scientific notation of the form:

1.xxxx×2n

Converting 1001.112 into scientific notation gives:

1001.112=1.001112×23

The exponent is 3 (because the binary point is shifted 3 places to the left).

✅ Step 2: Convert the Exponent to Binary

The exponent is 3 in decimal. To represent this in binary using 6 bits, we get:

Exponent=0001002

✅ Step 3: Convert the Fraction to 8 Bits

The fractional part of the normalized binary number is 00111. We need to extend it to 8 bits:

Fraction=010011102

✅ Final Answer:

The floating-point binary number +1001.112 in 8-bit fraction and 6-bit exponent format is:

Exponent: 0001002, Fraction: 010011102



Consider the equation (40)x = (132)y is some bases x and y. Then a possible set of value of x and y are





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Solution

(40)x=(132)y4×x1+0×x0=1×y2+3×y1+2×y04x+0=y2+3y+24x=y2+3y+2


Suppose we have a 10-bit computer that uses 10-bit int (2's complement representation). the number representation of - 35 is





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Solution

10-bit 2's Complement Representation of –35

Format: 10-bit signed integer using 2's complement representation.

Step-by-Step:

  1. First, convert 35 to 10-bit binary: 0000100011
  2. Find 1's complement: 1111011100
  3. Add 1 (to get 2's complement): 1111011101

✅ Final Answer: 1111011101

 –35 in 10-bit 2's complement: 1111011101



What is a potential problem of 1’s complement representation of numbers?





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Solution



In IEEE single precision floating point representation, exponent is represented in ______





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Solution



With 4-bit 2's complement arithmetic, which of the following addition will result in overflow?





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Solution



If the 2's complement representation of a number is (011010)2 , what is its equivalent hexadecimal representation?       





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Solution

2's Complement to Hexadecimal Conversion

Given the 2's complement binary number: (011010)
Find its equivalent hexadecimal representation.

Since the number has 6 bits, group the bits into two groups of 4 bits (add leading zeros if needed):
(011010)2=(00011010)2

Now, split into two nibbles (4 bits each):
00011010

Convert each nibble to hexadecimal:
- 00012=116
- 10102=A16

Therefore, the hexadecimal representation is: 1A



The base ( or radix) of the number system such that the following equation holds 312/20 = 13.1 is





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Solution



Which of the following represents (D4)16 ?





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Solution



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