Dear Students,
SBI has
included Computer Aptitude questions in place of
the general computer awareness questions in mains exam
of State Bank of India PO. Now, new types of questions will be asked in the
Computer sections which will be mainly based on conversion from Binary to Decimal & vice versa.
The questions
will be asked in the form of Puzzle, so don't confuse in between Computer Awareness & Computer Aptitude.
Data Representation
To know data
representation in the computer we must know following number systems.
- Decimal number system (Base=10): 0,1,2,3,4,5,6,7,8,9
- Binary number system (Base=2): 0,1
- Octal number System (Base=8): 0,1,2,3,4,5,6,7
- Hexa Decimal System (Base=16): 0,1,2,3,4,5,6,7,8,9, A(10),B(11),C(12),D(13),E(14),F(15)
Decimal to Binary Conversion: To convert 207 to binary
- Start with the digit farthest to the left.
- Determine if the decimal value can be divided by it.
- Since it will go one time, put a 1 in row three of the conversion table under the 128 value and calculate the remainder, 79.
- Since the remainder can be divided by the next value, 64, put a 1 in row three under the 64 value of the table.
- Since the remainder cannot be divided by either 32 or 16, put 0s in row three of our table under the 32 and 16 values.
- Continue until there is no remainder.
- If necessary, use row four to check the work.
|
Position
|
8
|
7
|
6
|
5
|
4
|
3
|
2
|
1
|
|
Value
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
|
|
128
|
64
|
8
|
4
|
2
|
1
|
128+ 64+
8+ 4 + 2 +1 =207
Binary to Decimal Conversion: To convert 10111001 to decimal
- Enter the binary bits in row three. In this example 10111001
- Put the decimal values in row four only for the third row 1s. Technically the row two values are being multiplied by row three.
- Now just add row four across.
|
Position
|
8
|
7
|
6
|
5
|
4
|
3
|
2
|
1
|
|
Value
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
|
|
128
|
32
|
16
|
8
|
1
|
128+32+16+8+1=
185
In summary, to convert from one number to another we can
use the following rule:
Hexadecimal
<-> Binary <-> Decimal
Direction: (1 -5): Read the following
information and answer the questions
In a certain
code language, the symbol for '0' is © and for '1' is '#'.
There are no other symbols for numbers greater than one. The numbers greater
than one is to be written only by using the two symbols given above. The value
of symbol for '1' doubles itself every time it shifts one place to the left.
Study the following examples:
0 is written as ©, 1 is written as #, 2 is written as #©, 3 is written as ##, 4 is written as #©© and so on.
1. Which of the following represents 25?
(1) ## © © #
(2) # © © ©
#
(3) ### © ©
(4)© ##©#
(5) ##© ©©
Ans: (1)
25 can
be written in binary form as follows:
= 24+ 23 +(0x22) + (0x21)
+ 1x20
## © © #
2. Which of the following will represent the value of (# ©
# x ## ©)?
(1) # © # # ©
(2) # © © # #
(3) © ### ©
(4)####©
(5) #####©
Ans: (4)
#©#= 22 + (0 x 21 ) + 20=5
##©= 22 +21+(0x20) = 6
(#©# X ##©) =
(5 x 6) = 30
30 can be
written in binary form as follows:
=24+ 23 +22+21+(0x20)
####©
3. Which of the following number will be represented by
##©#©#?
(1)
54
(2)
57
(3)
53
(4)
61
(5) 32
Ans: (3)
##©#©#
=25 +24+
(0 x 23) +22+(0
x 21) +20
= 53
4. Which of the following represents the value of {8x5}
÷2?
(1)
#©#©#
(2) ##©##©
(3) ©####©
(4)
#©#©©
(5) None of
these
Ans:(4)
{8 x 5÷2} =20
20 can be
written in binary form as follows:
=24+ (0 x 23)
+22+(0 x 21)
+( 0 x 20 )
#©#©©
5. Which of the following number will be represented by
#©©#©#?
(1)
52
(2)
50
(3)
53
(4)
37
(5) 20
Ans: (4)
#©©#©#
=25 + (0 x 24 )+ (0 x 23) +22+(0
x 21) +20
37
Directions (6 -7): Read the following information and
answer the questions that follow:
Following
letters are to be coded as number codes by following the rule given below:
Letter code:
{G,D,H –1}
{P,K,Q – 2} {B,C,F – 3} {J,M,N – 4} {L,R,W – 5} {T,X,Y – 6} {V,Z,S – 7}
(1) If the word starts or ends with a
vowel, then it is coded as '9'.
(2) If the vowels are neither in the
beginning nor at the end, then it is coded as '8'.
(3) If the word starts and ends with the
same vowel, then it is coded as 'α'.
6. Which of the following is the code for ‘ELEVATE’?
(1) α 376374 α
(2) α58786α
(3) α 4263747
(4) α 3213747
(5) None of
these
Ans: (2)
ELEVATE - α58786α
7. Which of the following is the code for 'CRYPT'?
(1)
35626
(2)
82778
(3) 62776
(4)
62476
(5) None of
these
Ans: (1)
CRYPT- 35626
8. Convert (34510) to a binary number?
(1) 101011001
(2) 100001010
(3) 100101010
(4) 110001011
(5) None of
these
Ans: (1)
Step by step solution
Step 1: Divide (345)10 successively by 2 until the quotient
is 0:
- 345/2 = 172, remainder is 1
- 172/2 = 86, remainder is 0
- 86/2 = 43, remainder is 0
- 43/2 = 21, remainder is 1
- 21/2 = 10, remainder is 1
- 10/2 = 5, remainder is 0
- 5/2 = 2, remainder is 1
- 2/2 = 1, remainder is 0
- 1/2 = 0, remainder is 1
Step 2: Read from bottom (MSB) to top
(LSB) as 101011001. This is the binary equivalent of decimal number 345
(Answer).
9. Convert (13010) to a binary number?
(1)
1010110
(2) 1100010
(3) 10011010
(4)
10000010
(5) None of
these
Ans: (4)
Step by step solution
Step 1: Divide (130)10 successively by 2 until the
quotient is 0:
130/2 = 65, remainder is 0
65/2 = 32, remainder is 1
32/2 = 16, remainder is 0
16/2 = 8, remainder is 0
8/2 = 4, remainder is 0
4/2 = 2, remainder is 0
2/2 = 1, remainder is 0
1/2 = 0, remainder is 1
Step 2: Read from bottom (MSB) to top (LSB) as 10000010 (Answer).
This is the
binary equivalent of decimal number 130.
10. Convert (10011)2 to Decimal number system?
(1) 19
(2) 20
(3) 25
(4) 30
(5) None of
these
Ans: (1)
Step by step solution
Step1: Write down the binary number: 10011
Step 2: Multiply each digit of the binary
number by the corresponding power of two:
1x24 + 0x23 + 0x22 + 1x21 + 1x20 =
Step 3: Solve the powers:
1x16 + 0x8 +
0x4 + 1x2 + 1x1 = 16 + 0 + 0 + 2 + 1
Step 4: Add up the numbers written above:
16 + 0 + 0 + 2
+ 1 = 19.
This is the
decimal equivalent of the binary number 10011.
Solution: 1-(1); 2-(4); 3-(3); 4-(4); 5-(4); 6-(2); 7(1);
8(1);9(4);10(1);
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