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Number Systems
Place value
Place value is the value of each digit in a number. The value of every digit in a number is different based on its position. A number might have two similar digits but different values, which is decided by the position that the digit holds in the number.
Place Value and Face Value
Given the number is 5369.
Face value of 9 is 9 and Place value of 9 is 9
Face value of 6 is 6 and place value of 6 is 60 (Sixty)
Face value of 3 is 3 and place value of 3 is 300 (Three hundred)
Face value of 5 is 5 and place value of 5 is 5000 (Five thousand)
Therefore, we can see, the face value of the digits in number 5369 represents the actual value of the digit.
Representing numbers in Decimal Number System
2-digit number – 10x+y
3-digit number – 100x+10y+z
…
In general, a n-digit number
Representing numbers in any Number System
Watch the video to learn more.
Here’s the flashcard:
Conversion of Number Systems
Refer to the lecture for details.
0-40 in Different Number Systems (Flash Card)
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Convert to other number systems.
Hexadecimal: Show Answer
37
Decimal: Show Answer
55
Binary: Show Answer
67
Convert to other number systems.
Hexadecimal: Show Answer
A
Octal: Show Answer
12
Binary: Show Answer
1010
If 25 is written as
Then how will 101 be written? (CSIR-NET SEPT 2022 – CS)
1010101
That’s wrong! Is it a familiar number system?
1100111
That’s wrong! Is it a familiar number system?
1101101
That’s wrong! Is it a familiar number system?
1100101
Here, 25 is converted to binary form.
Consider a number 54 expressed in a base different from 10. What is the base of this number system if its equivalent value in the decimal system is 49? (CSIR-NET JUNE 2018)
1
That’s wrong! If x is the base, then … Then x is?
3
That’s wrong! If x is the base, then … Then x is?
6
That’s wrong! If x is the base, then … Then x is?
9
That’s right!
N is a two-digit number such that the product of its digits when added to their sum = N. The unit digit of N would be: (CSIR-NET JUNE 2017)
1
That’s wrong! Hint: Write N = 10x + y. Then Product of digits = xy and the Sum of digits = x + y.
7
That’s wrong! Hint: Write N = 10x + y. Then Product of digits = xy and the Sum of digits = x + y.
8
That’s wrong! Hint: Write N = 10x + y. Then Product of digits = xy and the Sum of digits = x + y.
9
That’s right!
Choose the four-digit number, in which the product of the first & fourth digits is 40 and the product of the middle digits is 28. The thousands digit is as much less than the unit digit as the hundreds digit is less than tens digit. (CSIR-NET JUNE 2016)
5478
That’s right!
5748
That’s wrong! Hint: The thousands digit is < Unit digit and hundreds digit is less than tens!
8745
That's wrong! Hint: The thousands digit is < Unit digit and hundreds digit is less than tens!
8475
That's wrong! Hint: The thousands digit is < Unit digit and hundreds digit is less than tens!
If D = ABC + BCA + CAB where A, B, C are decimal digits, then D is divisible by? (CSIR-NET DEC 2018)
37 and 29
That's wrong! Hint: Try taking the simplest example!
37 but not 29
That's right!
29 but not 37
That's wrong! Hint: Try taking the simplest example!
Neither 29 nor 37
That's wrong! Hint: Try taking the simplest example!
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to other number systems.
to other number systems.
… Then x is?
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