# 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

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

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

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

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 * 162 + 14 * 161 + 2 * 160 (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

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

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 * 81 + 4 * 80
= 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

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

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 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20 = 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

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