2.1 - Number Systems and boolean Algebra.

2.1.1 - Number System.

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• A) 2
• B) 8
• C) 10
• D) 16

• A) Decimal
• B) Octal
• C) Binary
• D) Hexadecimal

• A) 2
• B) 8
• C) 10
• D) 16

• A) 2
• B) 8
• C) 10
• D) 16

• A) 10²
• B) 10¹
• C) 10³
• D) 10⁴

• A) 2
• B) 8
• C) 10
• D) 16

• A) (101)₂
• B) (345)₈
• C) (23)₁₀
• D) (1A3)₁₆

• A) 1
• B) 2
• C) 4
• D) 8

• A) 2⁰
• B) 2¹
• C) 2²
• D) 2³

• A) (number)₁₀
• B) (number)₂
• C) (number)₈
• D) (number)₁₆

• A) 10^-2
• B) 10^-1
• C) 10⁰
• D) 10¹

• A) 2⁰
• B) 2¹
• C) 2²
• D) 2³

• A) 10
• B) 12
• C) 16
• D) 2

• A) Decimal
• B) Binary
• C) Octal
• D) Hexadecimal

• A) 10⁰
• B) 10¹
• C) 10²
• D) 10³

• A) 1/2
• B) 1/4
• C) 1/8
• D) 1/16

2.1.2 - Hexadecimal and Octal Number System.

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• A) 2
• B) 8
• C) 10
• D) 16

• A) 0 to 9
• B) 0 to 7
• C) 0 to F
• D) 1 to 8

• A) 8
• B) 10
• C) 12
• D) 16

• A) 273
• B) 103
• C) 8F7
• D) 2375

• A) E
• B) F
• C) D
• D) 9

• A) 10
• B) 11
• C) 12
• D) 13

• A) 1A2
• B) 29G
• C) 56H
• D) 12Z

• A) 8
• B) 10
• C) 18
• D) 7

• A) 5
• B) 7
• C) G
• D) D

• A) 8
• B) 10
• C) 12
• D) 16

• A) 8⁰
• B) 8¹
• C) 8²
• D) 8³

• A) 16⁰
• B) 16¹
• C) 16²
• D) 16³

• A) 9
• B) A
• C) F
• D) E

• A) 8⁰
• B) 8¹
• C) 8²
• D) 8³

• A) 13
• B) 14
• C) 15
• D) 16

• A) 0
• B) 1
• C) 2
• D) 3

• A) 6
• B) 7
• C) 8
• D) 9

• A) 1A2
• B) 137
• C) 8B7
• D) 29G

• A) 16⁰
• B) 16¹
• C) 16²
• D) 16³

• A) 14
• B) 15
• C) 16
• D) 17

2.1.3 - Conversion Between Number System.

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• A) Divide by 2
• B) Multiply by 2
• C) Divide by 8
• D) Multiply by 8

• A) Divide by 2
• B) Multiply by 2
• C) Divide by 8
• D) Multiply by 8

• A) Convert the decimal fraction portion
• B) Convert the decimal integer portion
• C) Combine both portions
• D) Multiply by the base

• A) Divide by 8
• B) Multiply by 8
• C) Divide by 16
• D) Multiply by 16

• A) 0.001111
• B) 0.100010
• C) 0.010111
• D) 0.111000

• A) Group the binary digits into groups of four bits
• B) Group the binary digits into groups of three bits
• C) Convert each group of four bits to decimal
• D) Divide the binary number by 8

• A) Octal
• B) Decimal
• C) Hexadecimal
• D) Binary

• A) Convert the integer portion to binary
• B) Convert the fraction portion to binary
• C) Convert the integer portion to hexadecimal
• D) Convert the fraction portion to hexadecimal

• A) Base 8
• B) Base 16
• C) Base 10
• D) Base 2

• A) 11.5625
• B) 10.6875
• C) 12.75
• D) 9.875

• A) Group the binary digits into sets of four
• B) Convert each group of four bits to a hexadecimal digit
• C) Convert each group of three bits to a hexadecimal digit
• D) Combine the hexadecimal digits

• A) Position increases to the left of the decimal point
• B) Position increases to the right of the decimal point
• C) Position decreases to the left of the decimal point
• D) Position decreases to the right of the decimal point

• A) Multiply by the base
• B) Divide by the base
• C) Find the sum of Face Value * (from Base) position
• D) Group digits into sets of four

• A) Group the binary digits into sets of three bits
• B) Group the binary digits into sets of four bits
• C) Convert each group of four bits to octal digits
• D) Convert each bit individually

• A) 20.4375
• B) 22.4375
• C) 20.75
• D) 18.75

2.1.4 - One's Complement.

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• A) 10101101
• B) 01010011
• C) 01010010
• D) 11100011

• A) Each 0 is converted to 1, and each 1 is converted to 0
• B) Each 0 is multiplied by 1, and each 1 is divided by 2
• C) Each bit is left unchanged
• D) Each bit is inverted and then multiplied by 2

• A) 1010.010
• B) 0010.010
• C) 0010.010
• D) 1110.111

• A) Representing signed binary numbers
• B) Binary arithmetic operations like addition
• C) Floating-point arithmetic operations
• D) Decimal to binary conversion

• A) 0101
• B) 1111
• C) 1010
• D) 0000

• A) 2⁵ - 1
• B) 2⁴ - 1
• C) 2⁴
• D) 2⁵

• A) 1111 1001
• B) 0000 0110
• C) 1111 1010
• D) 0000 1101

• A) It has two representations for zero: positive zero and negative zero
• B) It has a unique representation for zero
• C) It uses only unsigned binary numbers
• D) It can represent only negative numbers

• A) -8 to 7
• B) -7 to 7
• C) -8 to 8
• D) -7 to 8

• A) 1111 0101
• B) 1111 0100
• C) 1111 0110
• D) 0000 1010

2.1.5 - Two's Complemen.

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• A) Limited number of negative values
• B) Two representations of zero
• C) Cannot store positive values
• D) Sign extension works perfectly

• A) By flipping each bit of the positive number
• B) By adding 1 to the positive number
• C) By keeping the first bit as the sign bit
• D) By adding 2 to the positive number

• A) Two representations of zero
• B) Negative numbers work with signed extensions
• C) Binary addition doesn’t work
• D) Limited storage capacity for values

• A) Flip each bit of the positive number
• B) Flip each bit of the positive number and add 1
• C) Add 2 to the positive number
• D) Keep the sign bit and flip the other bits

• A) Multiple representations of zero
• B) Only one representation of zero
• C) Sign extension does not work
• D) Requires additional hardware

• A) When carry into the signed bit is equal to carry out
• B) By checking for multiple representations of zero
• C) By checking the first bit for the sign
• D) When all bits are set to 1

• A) Negative numbers do not support sign extension
• B) Two representations of zero
• C) Cannot represent positive numbers correctly
• D) Binary subtraction is not possible

• A) Stores the value of the number
• B) Indicates the sign of the number
• C) Determines if the number is odd or even
• D) Used for overflow detection

• A) The sign bit must be handled separately
• B) It produces overflow errors
• C) It cannot add negative numbers
• D) It requires extra bits

• A) It indicates the type of number
• B) All positive numbers start with 0, and all negative numbers start with 1
• C) It determines the number of bits to be used
• D) It shows the magnitude of the number

2.1.6 - Boolean Algebra and Laws.

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• A) Algebra involving decimal numbers and arithmetic operations
• B) Algebra involving binary variables and logic operations
• C) Algebra involving hexadecimal numbers and conversions
• D) Algebra involving algebraic expressions and equations

• A) A'
• B) A
• C) A''
• D) A bar

• A) OR operation
• B) AND operation
• C) NOT operation
• D) XOR operation

• A) OR operation
• B) AND operation
• C) NOT operation
• D) XOR operation

• A) All literals must be 1
• B) At least one literal must be 1
• C) All literals must be 0
• D) At least one literal must be 0

• A) All literals must be 1
• B) At least one literal must be 1
• C) All literals must be 0
• D) At least one literal must be 0

• A) Distributive Law
• B) Associative Addition Law
• C) Commutative Addition Law
• D) Associative Multiplication Law

• A) To perform an AND operation
• B) To perform an OR operation
• C) To produce the complement of a variable
• D) To combine multiple literals

• A) An OR operation
• B) A NOT operation
• C) An AND operation
• D) A sum term

• A) 2ⁿ
• B) n²
• C) 2ⁿ - 1
• D) n² - 1

• A) Identity Law
• B) Idempotent Law
• C) Complement Law
• D) Distribution Law

• A) For data conversion between number systems
• B) For performing binary arithmetic operations
• C) For manipulating binary data in circuits
• D) For encoding and decoding information

• A) It simplifies the representation of signed integers
• B) It provides easier arithmetic operations and overflow checks
• C) It allows for a larger range of positive numbers
• D) It is easier to convert between number systems

• A) The process of combining binary numbers
• B) The OR operation in Boolean algebra
• C) The AND operation in Boolean algebra
• D) The process of finding the complement of a variable

• A) Decimal
• B) Binary
• C) Octal
• D) Hexadecimal