**Digital Circuits Questions and Answers – Number System – 2**

This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Number System – 2”.

**1. The given hexadecimal number (1E.53)16 is equivalent to ____________**

a) (35.684)8

b) (36.246)8

c) (34.340)8

d) (35.599)8

**Answer:** **b**

**Explanation:** First, the hexadecimal number is converted to it’s equivalent binary form, by writing the binary equivalent of each digit in form of 4 bits. Then, the binary equivalent bits are grouped in terms of 3 bits and then for each of the 3-bits, the respective digit is written. Thus, the octal equivalent is obtained.

(1E.53)16 = (0001 1110.0101 0011)2

= (00011110.01010011)2

= (011110.010100110)2

= (011 110.010 100 110)2

= (36.246)8

**2. The octal number (651.124)8 is equivalent to ______**

a) (1A9.2A)16

b) (1B0.10)16

c) (1A8.A3)16

d) (1B0.B0)16

**Answer: a**

**Explanation:** First, the octal number is converted to it’s equivalent binary form, by writing the binary equivalent of each digit in form of 3 bits. Then, the binary equivalent bits are grouped in terms of 4 bits and then for each of the 4-bits, the respective digit is written. Thus, the hexadecimal equivalent is obtained.

(651.124)8 = (110 101 001.001 010 100)2

= (110101001.001010100)2

= (0001 1010 1001.0010 1010)2

= (1A9.2A)16

**3. The octal equivalent of the decimal number (417)10 is _____**

a) (641)8

b) (619)8

c) (640)8

d) (598)8

**Answer:** **a**

**Explanation:** Octal equivalent of decimal number is obtained by dividing the number by 8 and collecting the remainders in reverse order.

8 | 417

8 | 52 — 1

8 | 6 – 4

So, (417)10= (641)8

**4. Convert the hexadecimal number (1E2)16 to decimal:**

a) 480

b) 483

c) 482

d) 484

**Answer:** **c**

**Explanation:** Hexadecimal to Decimal conversion is obtained by multiplying 16 to the power of base index along with the value at that index position.

(1E2)16 = 1 * 16^{2} + 14 * 16^{1} + 2 * 16^{0} (Since, E = 14)

= 256 + 224 + 2 = (482)10

**5. (170)10 is equivalent to**

a) (FD)16

b) (DF)16

c) (AA)16

d) (AF)16

**Answer:** **c**

**Explanation:** Hexadecimal equivalent of decimal number is obtained by dividing the number by 16 and collecting the remainders in reverse order.

16 | 170

16 | 10 – 10

Hence, (170)10 = (AA)16

**6. Convert (214)8 into decimal:**

a) (140)10

b) (141)10

c) (142)10

d) (130)10

**Answer:** **a**

**Explanation:** Octal to Decimal conversion is obtained by multiplying 8 to the power of base index along with the value at that index position.

(214)8 = 2 * 8v + 1 * 8^{1} + 4 * 8^{0}

= 128 + 8 + 4 = (140)10

**7. Convert (0.345)10 into an octal number:**

a) (0.16050)8

b) (0.26050)8

c) (0.19450)8

d) (0.24040)8

**Answer:** **b**

**Explanation: **Converting decimal fraction into octal number is achieved by multiplying the fraction part by 8 everytime and collecting the integer part of the result, unless the result is 1.

0.345*8 = 2.76 2

0.760*8 = 6.08 6

00.08*8 = 0.64 0

0.640*8 = 5.12 5

0.120*8 = 0.96 0

So, (0.345)10 = (0.26050)8

**8. Convert the binary number (01011.1011)2 into decimal:**

a) (11.6875)10

b) (11.5874)10

c) (10.9876)10

d) (10.7893)10

**Answer: a**

**Explanation**: Binary to Decimal conversion is obtained by multiplying 2 to the power of base index along with the value at that index position.

(01011)2 = 0 * 2^{4} + 1 * 2^{3} + 0 * 2^{2} + 1 * 2^{1} + 1 * 2^{0} = 11

(1011)2 = 1 * 2^{-1} + 0 * 2^{-2} + 1 * 2^{-3} + 1 * 2^{-4} = 0.6875

So, (01011.1011)2 = (11.6875)10

**9. Octal to binary conversion: (24)8 =?**

a) (111101)2

b) (010100)2

c) (111100)2

d) (101010)2

**Answer:** **b**

**Explanation:** Each digit of the octal number is expressed in terms of group of 3 bits. Thus, the binary equivalent of the octal number is obtained.

(24)8 = (010100)2

**10. Convert binary to octal: (110110001010)2 =?**

a) (5512)8

b) (6612)8

c) (4532)8

d) (6745)8

**Answer:** b

**Explanation:** The binary equivalent is segregated into groups of 3 bits, starting from left. And then for each group, the respective digit is written. Thus, the octal equivalent is obtained.

(110110001010)2 = (6612)8

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