# Computer Fundamentals Questions and Answers – The Octal Number System

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This set of Computer Fundamentals Multiple Choice Questions & Answers (MCQs) focuses on “The Octal Number System”.

1. What could be the maximum value of a single digit in an octal number system?
a) 8
b) 7
c) 6
d) 5

Explanation: The maximum value in any number system is one less than the value of the base. The base in an octal number system is 8, therefore, the maximum value of the single digit is 7. It takes digits from 0 to 7.

2. In a number system, each position of a digit represents a specific power of the base.
a) True
b) False

Explanation: In a number system, every digit is denoted by a specific power of base. Like in an octal system, consider the number 113, it will be represented as :
82 * 1 + 81 * 1 + 80 *3.

3. The maximum number of bits sufficient to represent an octal number in binary is _______
a) 4
b) 3
c) 7
d) 8

Explanation: The octal number system comprises of only 8 digits. Hence, three bits (23 = 8) are sufficient to represent any octal number in the binary format.

4. The binary number 111 in octal format is ________________
a) 6
b) 7
c) 8
d) 5

Explanation: Certain binary to octal representations are :
000=0
001=1
010=2
011=3
100=4
101=5
110=6
111=7.

5. Convert (22)8 into its corresponding decimal number.
a) 28
b) 18
c) 81
d) 82

Explanation: To convert an octal number to decimal number:
81 * 2 + 80 * 2 = 16 + 2 = 18.
Hence, the decimal equivalent is 18.

6. The octal equivalent of the binary number (0010010100)2 is ______________
a) 422
b) 242
c) 224
d) 226

Explanation: To obtain the octal equivalent, we take numbers in groups of 3, from right to left as :

``` 000  010  010   100

0    2    2      4     =  (224)<sub>8</sub>.```

7. Octal subtraction of (232)8 from (417)8 will give ______________
a) 165
b) 185
c) 815
d) 516

Explanation: Octal subtraction is done as follows:
417
– 232
________
165
The octal subtraction is the same as that of any other number system. The only difference is, like in a decimal number system, we borrow a group of 10, in a binary system we borrow a group of 2, in an octal number system, we borrow in groups of 8.

8. The 1’s complement of 0.101 is _________________
a) 1.010
b) 0.010
c) 0.101
d) 1.101

Explanation: The 1’s complement of a number is obtained by reversing the bits with value 1 to 0 and the bits with value 0 to 1.
Here, 0.101 gets converted to 1.010 in its 1’s complement format.

a) A01
b) A02
c) B01
d) C01

Explanation: To convert octal to hexadecimal, we first write binary format of the number and then make groups of 4 bits from right to left, as follows:

``` 5     4      0     1
101   100    000    001   (octal -> binary)
1011     0000    0001     ( groups of 4)
B         0       1       ( hexadecimal equivalent)```

Therefore, the hexadecimal equivalent is (B01)16.

10. Express the decimal format of the signed binary number (10010)2 .
a) 2
b) 12
c) -12
d) -2

Explanation: The first bit is the sign bit whereas the rest of the bits are magnitude bits. So the number is: 0010 = 21 * 1 =2
But, the sign bit is 1, Therefore the answer is : (-2)10.

Sanfoundry Global Education & Learning Series – Computer Fundamentals.

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