Question

3. Choose the correct option.

a. Which of the following decimal numbers is equivalent to 11111,?
i. 30 ii. 31 iii. 32 iv. 33

b. Which of the following numbers have the MSD as 7?
i. 7A.CD ii. 72.34 iii. 79.45 iv.. All of them

c Which one is not a correct octal number?
i 65.32 ii. 82.21 iii. 56.34 iv. 12.54

d. The equivalent binary number of 47 is:
i. 101111 ii. 110111 iii. 111011 iv. 111101

e. Which of these is not an example of application software?
i. Windows 10 ii. Payroll iii. Inventory iv. Report Card​

Answer 1

The correct option are as follows :

For (a)

Answer : (ii) 31

For (b)

Answer : (iv) 31

For (c)

Answer : (ii) 82.21

For (d)

Answer : (i) 101111

For (e)

Answer : (iv) Report card.

Answer 2

• 31 is  decimal numbers is equivalent to 11111
• 7A.CD , 72.24 and 79.45 all have MSD (Most significant digit) as 7
• 82.21 is not a correct octal number
• The equivalent binary number of 47 is: 101111
• Windows 10 is not an example of application software

Need to find Equivalent Decimal for given binary number 11111.

Equivalent Decimal is

1*2⁴ + 1*2³ + 1*2² + 1*2¹ + 1*2⁰

16 + 8 + 4 + 2 + 1

31

Hence correct option is ii. 31

About significant digits

All non-zero digits are significant.

The leftmost nonzero digit is the first or most significant digit/figure.

If there is a decimal point, the rightmost digit is the last or least significant figure

If there is no decimal point explicitly shown, the rightmost non-zero digit is the least significant figure

All digits between the most significant figure and the least significant figure are significant.

Given Numbers are:

• 7A.CD
• 72.34
• 79.45

All given numbers has left most non zero digit as 7

Therefore , all have MSD ( most significant digit as 7)

Hence  iv.. All of them  is correct option

Octal numbers has digit 0 to 7

Hence option  ii) 82.21  is not correct octal

The equivalent binary number of 47 is: 101111

This can be obtained by Division algorithm as below

       47     Remainder

2     23       1

2      11        1

2       5        1

2       2        1

 2       1       0

 2       0       1

Read remainders from bottom to up   (101111)

Windows 10 is an operating system not an application software

Hence i) windows  10  is correct option