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Questions and Answers

What is the hexadecimal equivalent of the binary number 11010011100100101011?

  • 0xB392D
  • 0xD392B (correct)
  • 0xD32B9
  • 0xD239B

Which of the following represents the decimal equivalent of the hexadecimal digit 'B'?

  • 14
  • 12
  • 13
  • 11 (correct)

What does the prefix '0x' signify when placed before a number?

  • That the number is in hexadecimal format (correct)
  • That the number is in decimal format
  • That the number is in octal format
  • That the number is in binary format

In the binary to hexadecimal conversion process, what is done during Step 1?

<p>Segment the binary into four bits (D)</p> Signup and view all the answers

What is the binary equivalent of the hexadecimal digit 'E'?

<p>1110 (B)</p> Signup and view all the answers

What process is used to convert hexadecimal to decimal?

<p>Adding the decimal equivalent of each hex digit (C)</p> Signup and view all the answers

In the conversion table, what is the decimal equivalent of 'F'?

<p>15 (A)</p> Signup and view all the answers

What is the primary advantage of using Unicode over previous encoding systems?

<p>It can represent a larger number of unique symbols. (C)</p> Signup and view all the answers

Which statement accurately describes records and files in data processing?

<p>The organization of data in a record is determined by the programming language. (B)</p> Signup and view all the answers

What is the primary purpose of registers in a CPU?

<p>To provide fast access to commonly used values. (B)</p> Signup and view all the answers

How is the size of registers typically measured?

<p>By the number of bits they can store. (C)</p> Signup and view all the answers

Which of the following best describes the two kinds of registers mentioned?

<p>General Purpose Registers are accessible to programmers, while others are not. (C)</p> Signup and view all the answers

What does a sign bit value of 1 indicate in a floating point binary representation?

<p>The number is negative (C)</p> Signup and view all the answers

In the bit stream 01011101, how many bits are allocated for the mantissa?

<p>4 bits (A)</p> Signup and view all the answers

Which part of the bit stream specifically indicates the value greater than one?

<p>Exponent (D)</p> Signup and view all the answers

What is the decimal equivalent of the binary bit stream 101.1101?

<p>5.8125 (B)</p> Signup and view all the answers

What type of error might arise due to the limited number of bits used in floating point representation?

<p>Truncation error (B)</p> Signup and view all the answers

How many bits are typically used in modern computers to represent floating point values?

<p>32 bits (A)</p> Signup and view all the answers

Which of the following represents the mantissa segment in the binary representation 01011101?

<p>1101 (B)</p> Signup and view all the answers

What is the maximum possible value for the exponent using a 3-bit exponent field?

<p>7 (D)</p> Signup and view all the answers

In the conversion of 101.1101 to decimal, which part contributes to the fraction?

<p>The mantissa (C)</p> Signup and view all the answers

What base is primarily used for the binary representation of data in computing?

<p>Base 2 (D)</p> Signup and view all the answers

What is the primary limitation of the ASCII coding system?

<p>It is unable to represent languages with large alphabets. (D)</p> Signup and view all the answers

Which of the following characters can be represented by ASCII?

<p>Uppercase alphabets (A)</p> Signup and view all the answers

How many bits does the ASCII coding system use to represent each character?

<p>7 bits (D)</p> Signup and view all the answers

What is the binary representation of the character 'E' in ASCII?

<p>1000101 (A)</p> Signup and view all the answers

What decimal value corresponds to the ASCII representation of the character 'l'?

<p>108 (D)</p> Signup and view all the answers

Which of the following represents the ASCII code for the exclamation mark '!'?

<p>33 (B)</p> Signup and view all the answers

In the binary ASCII representation, which of the following correctly represents the combination for the lowercase 'd'?

<p>1100100 (A)</p> Signup and view all the answers

What aspect differentiates the ASCII codes for uppercase and lowercase letters?

<p>Their decimal values differ by a fixed range (D)</p> Signup and view all the answers

Which of the following is true about non-numeric data representation?

<p>They require a unique coded format for representation. (A)</p> Signup and view all the answers

What does ANSI stand for in the context of ASCII?

<p>American National Standards Institute (B)</p> Signup and view all the answers

What is the hexadecimal representation of the decimal number 734593?

<p>0xB3581 (C)</p> Signup and view all the answers

Which of the following numbers qualifies as an integer?

<p>0 (A)</p> Signup and view all the answers

In two's complement notation, how is a positive number represented?

<p>Using a leading 0 (B)</p> Signup and view all the answers

Which of the following is NOT an integer?

<p>5/6 (D)</p> Signup and view all the answers

What is the purpose of flipping bits in two's complement notation?

<p>To create a negative representation (B)</p> Signup and view all the answers

How many bits are commonly used today to represent integers in computers?

<p>32 bits (C)</p> Signup and view all the answers

Which operation is the final step in finding the two's complement of a binary number?

<p>Adding 1 to the last bit (C)</p> Signup and view all the answers

Which of the following is a correct representation of the set of integers, Z?

<p>{..., -3, -2, -1, 1, 2, 3, ...} (D)</p> Signup and view all the answers

When converting a decimal number to hexadecimal, what is the base used for division?

<p>16 (D)</p> Signup and view all the answers

Flashcards

Hexadecimal Number

A base-16 number system that uses digits 0-9 and letters A-F to represent values.

Nibble

A group of four bits in a binary number.

Binary to Hexadecimal Conversion

The process of converting a binary number to its hexadecimal equivalent.

Hexadecimal to Decimal Conversion

The process of converting a hexadecimal number to its decimal equivalent.

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0x Prefix

A prefix used to indicate that a number is in hexadecimal format.

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Bit Position

The position of a digit in a number, starting from 0 for the least significant bit.

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Number Base Conversion

The process of converting a number from one base to another, such as binary to hexadecimal or hexadecimal to decimal.

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Hexadecimal Number System

A number system with base 16, using digits from 0 to 9 and letters from A to F to represent values from 10 to 15.

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Integer

A whole number that can be positive, negative, or zero.

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Two's Complement Notation

A method of representing integers in binary using a fixed number of bits. The leftmost bit represents the sign (0 for positive, 1 for negative).

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Finding Two's Complement

The process of converting a positive number to its two's complement form. It involves flipping all the bits and adding 1 to the least significant bit.

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Binary Number System

A method of representing numbers using only 0's and 1's.

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Binary to Decimal Conversion

The process of converting a binary number to its decimal equivalent.

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Byte

A unique combination of 8 bits representing a character, symbol, or other data element.

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Sign Bit

The highest order bit in a floating-point number system, representing the sign (positive or negative).

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Exponent

A section of bits in a floating-point number that denotes the magnitude of the number. It's used to position the decimal point (or binary point).

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Mantissa

A section of bits in a floating-point number that holds the fractional part of the number.

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Decimal Equivalent

Converting a floating-point number representation back into its decimal equivalent.

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Truncation Error or Round-off Error

Error introduced in floating-point representation due to limitations in the number of bits used for the mantissa (truncating or rounding off decimal values).

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Number Bases

A way to represent data using different bases, such as binary (base 2), decimal (base 10), and hexadecimal (base 16).

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Binary (Base 2)

A number system with two digits (0 and 1), used for representing data in computers.

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Decimal (Base 10)

A number system with 10 digits (0-9) commonly used in everyday life.

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Hexadecimal (Base 16)

A number system with 16 digits (0-9 and A-F), often used in computer programming.

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Representation of Non-Numeric Data

A way to represent data using characters, symbols, and numbers.

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Record

A combination of different data objects (integers, floating-point numbers, character strings) organized for processing by a program.

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File

A collection of multiple records, often referred to as a data set.

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Register

A type of memory built into the CPU for faster access to frequently used values.

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General Purpose Registers

A set of registers accessible to programmers, used for general data processing.

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Special Purpose Registers

A set of registers not accessible to programmers, used for interpreting and executing instructions.

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What is non-numeric data?

Non-numeric data refers to data that cannot be represented as numbers and cannot be ordered sequentially based on their values. Examples include alphabets, special characters, images, and sound.

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What is ASCII?

The American Standard Code for Information Interchange (ASCII) is a widely adopted standard that uses a coded format to represent characters like letters, punctuation marks, and control functions on a keyboard. This code uses seven bits to represent each character.

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How are ASCII codes for alphabets organized?

ASCII codes for alphabets follow a sequential order based on their alphabetical position. This means you can easily determine the code for any letter if you know the codes for 'A' and 'a'.

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What is the difference between the decimal and binary number systems, and how do you convert between them?

The decimal number system is a base-10 system, while the binary number system is a base-2 system. To convert a decimal number to its binary equivalent, you repeatedly divide the decimal number by 2 and write down the remainders in reverse order.

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What is a limitation of ASCII?

The ASCII code uses a limited number of bits, which restricts its ability to represent a wide range of characters, such as those found in languages like Chinese and Japanese.

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Study Notes

Hexadecimal Numbers

  • Hexadecimal numbers use 16 different states/numerals
  • They combine the first ten numerals of decimal numbers and the first six alphabets
  • Table 2.3 shows the hexadecimal and decimal equivalents

Converting Binary to Hexadecimal

  • Prefix "0x" indicates a hexadecimal number (e.g., 0x3A7)
  • Divide the binary number into sections of four bits (nibbles)
  • Convert each nibble to its hexadecimal equivalent using Table 2.4
  • Example: Converting 11010011100100101011 to hex involves segmenting it into 1101, 0011, 1001, 0010, 1011

Converting Hexadecimal to Decimal

  • Number each numeral starting from 0 (least significant bit)
  • Table 2.4 shows the conversion of 0xD392B to decimal
  • Conversion formula example: D(13) x 164 + 3 x 163 + 9 x 162 + 2 x 161 + B(11) x 160 = 866603

Conversion of Decimal to hexadecimal

  • Repeatedly divide the decimal number by 16
  • Write down the remainders in reverse order
  • The remainders represent the hexadecimal digits

Integers

  • Integers are whole numbers (positive, negative, or zero)
  • Examples: -6, 2, 8, -95, 2015
  • The set of integers is denoted by Z: Z = {..., -3, -2, -1, 0, 1, 2, 3 ...}
  • Integers in computers are represented using two's complement and excess notations

Two's Complement Notation

  • Computers use a fixed number of bits to represent integers.
  • The most significant bit (leftmost) represents the sign (0 for positive, 1 for negative).
  • Steps to find the two's complement of a positive number:
    1. Find its binary equivalent
    2. Flip all the bits (0 to 1, 1 to 0)
    3. Add 1 to the least significant bit

Excess Notation

  • Another method for representing integers
  • The bit pattern length is determined and the bit patterns are listed.
  • The point where the most significant bit changes sign designates the split between positive and negative integers

Floating-Point Numbers

  • Floating-point numbers have a fractional part
  • Represented in floating-point notation
  • Sign bit (0 for positive, 1 for negative)
  • Exponent (holds the part greater than one)
  • Mantissa (holds the fractional part less than one)
  • Example: 01011101 is a positive bit stream with 101 as the exponent and 1101 as the Mantissa.
  • Converting floating point notations to decimal numbers requires a conversion table.

Non-Numeric Data

  • Non-numeric data includes alphabets, special characters, images, and sound
  • Not sequentially ordered based on values
  • Coded formats represent alphabets and special characters (e.g. ASCII)

Computer Records

  • Records are combinations of different data objects (integers, floating-point numbers, character strings)
  • Used for program processing
  • Can have fixed or variable lengths

Registers

  • High-speed memory built into the CPU
  • Used for quickly accessing commonly used values
  • Examples of registers: Accumulator (AC), Data Register (DR), Temporary register (TR), Instruction Register (IR), Address Register (AR), Program Counter (PC), Input Register (INPR) Output Register(OUTR)
  • Registers have different sizes

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