Introduction to Information Technology · Unit 2
Number Systems and Data Representation
Exam-focused notes for Number Systems and Data Representation (Introduction to Information Technology, BIT101): what the TU syllabus asks and how it has actually been tested, with 9 solved past questions from this unit.
What this unit covers
- Face value and position value concepts
- Binary number system and encoding
- Octal and hexadecimal number systems
- Base conversion between decimal, binary, octal, hexadecimal
- Binary arithmetic and operations
- Two's complement method for signed numbers
- Reasons for using hexadecimal and octal in computers
Two's complement method for signed numbers
Add number +7 and -17 using 2's complement method. [5]
- First number: $+7$ - Second number: $-17$ - Method: 2's complement addition - Using 8-bit representation (needed since $17$ requires 5 bits, plus sign bit). $+7$: $$+7 = 0000\ 0111$$ $+17$ (magnitude of the negative number): $$+17 = 0001\ 0001$$ 1's compl...
Full solved answer →Reasons for using hexadecimal and octal in computers
Explain the reason of using hexadecimal and octal number system in computer? Add decimal number 23 and 12 using binary addition and verify the result with the help of decimal system.[10]
- Task 1: Explain why hexadecimal (base-16) and octal (base-8) number systems are used in computers. - Task 2: Add decimal numbers $23$ and $12$ using binary addition and verify with the decimal system. - Numeric inputs: $23{10}$ and $12{10}$. All required ...
Full solved answer →Binary number system and encoding
What is Binary Encoding? Why computers use Binary Encoding? [5]
Binary Encoding is a method of representing data, numbers, characters, and instructions using only two symbols: 0 and 1 (bits). Every piece of information stored or processed in a computer is ultimately converted into a sequence of these two binary digits. ...
Full solved answer →Binary arithmetic and operations
Subtract 10010 from 10101. Verify answer with the help of decimal substraction. [5]
Binary Decimal Equivalent ---------------------------- $10101$ $16+0+4+0+1 = 21$ $10010$ $16+0+0+2+0 = 18$ We must compute $10101 - 10010$. --- Working right to left (bit 0 = LSB): Bit Minuend Subtrahend Operation Result ------------------------------------...
Full solved answer →Base conversion between decimal, binary, octal, hexadecimal
Convert 3748.658 decimal to Binay, Octal and Hexadecimal. [5]
- Decimal number: $3748.658$ - Integer part: $3748$ - Fractional part: $0.658$ - Convert to: Binary (base 2), Octal (base 8), Hexadecimal (base 16) --- Division Quotient Remainder ------------------------------- 3748 ÷ 2 1874 0 1874 ÷ 2 937 0 937 ÷ 2 468 1 ...
Full solved answer →Convert 44.467 from Base 10 to Base 16. [5]
- Number to convert: $44.467{10}$ - Target base: 16 Division Quotient Remainder Hex ------------------------------------ $44 \div 16$ 2 12 C $2 \div 16$ 0 2 2 Reading remainders bottom to top: $$44{10} = 2C{16}$$ Multiplication Product Integer part Hex ----...
Full solved answer →Convert $(366)_8$ to hexadecimal. Subtract $(1001111)_2$ from $(1110111)_2$. [2+3]
- Octal number to convert: $(366)8$ - Binary subtraction: $(1110111)2 - (1001111)2$ --- (a) Convert $(366)8$ to Hexadecimal Method: Octal → Binary → Hexadecimal Step 1: Each octal digit to 3-bit binary Octal Binary --------------- 3 011 6 110 6 110 $$(366)8...
Full solved answer →Convert 34.4674 from Base 10 to Base 16 [5]
- Decimal number: $34.4674$ - Target base: $16$ (hexadecimal) --- Divide repeatedly by 16, record remainders: Division Quotient Remainder ------------------------------- $34 \div 16$ $2$ $2$ $2 \div 16$ $0$ $2$ Reading remainders bottom to top: $$34{10} = 2...
Full solved answer →Face value and position value concepts
Explain the significance of the face value and position value of a number with an example. Convert the decimal number 47 into binary, octal and hexadecimal. [5]
- Number to convert: decimal $47$ - Target bases: binary (2), octal (8), hexadecimal (16) The face value of a digit is the intrinsic value of the digit itself, independent of where it appears in the number. It remains constant. Example: In the number $523$ ...
Full solved answer →Make Unit 2 stick
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