Number Systems

Number Systems in Computer Sciences

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Multiple Choice

How many types of Number systems are there?

• 1

• 2

• 3

• 4

Multiple Choice

Which set of Number systems is correct?

• Positional & Non-positional

• Binary, Decimal and Octal

• Hexadecimal

• None of above

Multiple Choice

How many Number systems are there in Computer Sciences

• 1

• 2

• 3

• 4

Multiple Choice

Which Number system do we use in our daily life?

• Binary

• Decimal

• Octal

• Hexa-decimal

Hexa-decimal Number System

BASE = 16

DIGITS = 0 - 9 and A,B,C,D,E,F for 10-15

Multiple Choice

9AF is a __ Number

• Binary

• Octal

• Hexa-decmial

• Decimal

Any Base to Decimal

Binary Example

(10101)₂ = (1 x 2⁴) + (0 x 2³) + (1 x 2²) + (0 x2¹)x(1x 2⁰)

= 16 + 0 + 4 + 0 + 1

= (21)₁₀

Octal Example

(4706)₈ = (4 x 8³) + (7 x 8²) + (0 x 8¹) + ( 6 x 8⁰)

= 2048 + 448 + 0 + 6

= (2502)₁₀

Multiple Choice

By Converting ( 1001 ) ₂ into decimal we will get __

• 9

• 11

• 12

• 16

Multiple Choice

By converting (2057)₈ into decimal we will get __

• 1071

• 1000

• 962

• none of above

Multiple Choice

By converting (100)₁₀ into binary we will get __

• (0110 0100)₂

• (64)₁₆

• (1001 1011)₂

• Both A and B

Fractional convertion Any base to Decimal

Octal Example

(127.54)₈ = (1 x 8²) + (2 x 8¹) + ( 7 x 8⁰) + (5 x 8^-1) + (4 x 8^-2)

= 64 + 16 + 7 + 0.625 + 0.0625

= (87.6875)₁₀

Multiple Choice

By converting 127.54₈ we will get _

• 87.6875₁₀

• 100.89₁₆

• both A and B

• none of above