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Questions and Answers

What is the result of the arithmetic operation 10010 - 11001?

  • 10111
  • -00111 (correct)
  • 00111
  • -10111

When dividing binary numbers, what indicates that the quotient is 1?

  • A borrow was needed during the subtraction step. (correct)
  • No borrow was needed during the subtraction step.
  • The dividend is smaller than the divisor.
  • The divisor is smaller than the dividend.

In the division of binary numbers, what must be done after subtracting the divisor from the dividend if a borrow was required?

  • Drop the next significant bit of the divisor and subtract the dividend from the result.
  • Drop the next significant bit of the divisor and add the dividend to the result.
  • Drop the next significant bit of the dividend and subtract the divisor from the result.
  • Drop the next significant bit of the dividend and add the divisor to the result. (correct)

Which of these is NOT a step involved in binary multiplication?

<p>Subtract the divisor from the dividend and add the result to the quotient. (D)</p> Signup and view all the answers

What is the 1's complement of the binary number 11001?

<p>00110 (D)</p> Signup and view all the answers

In binary addition, the overflow bit, which is the most significant bit, is ignored after the addition. What does it indicate?

<p>The addition was performed correctly. (B)</p> Signup and view all the answers

When performing binary division, why is it important to remove leading zeros from both the dividend and the divisor?

<p>To ensure that the division is performed correctly. (C)</p> Signup and view all the answers

What is the decimal equivalent of the hexadecimal number 0xB3581?

<p>734593 (D)</p> Signup and view all the answers

What is the hexadecimal equivalent of the decimal number 123456?

<p>0x1E240 (B)</p> Signup and view all the answers

In two's complement notation, what is the binary representation of the integer -5, assuming a 4-bit system?

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

Which of the following is NOT an example of an integer?

<p>-2.37 (B)</p> Signup and view all the answers

In the hexadecimal representation, what is the decimal equivalent of the character 'B'?

<p>11 (C)</p> Signup and view all the answers

Given the hexadecimal number 0xD392B, what is the value of the least significant digit in decimal?

<p>11 (C)</p> Signup and view all the answers

What is the decimal value of 16^2?

<p>256 (A)</p> Signup and view all the answers

When converting a decimal number to hexadecimal, why is the remainder written from last to first?

<p>It ensures the correct representation of the decimal number. (A)</p> Signup and view all the answers

In two's complement notation, what is the maximum positive integer representable using 4 bits?

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

What is the purpose of the most significant bit in two's complement notation?

<p>To indicate the sign of the number. (A)</p> Signup and view all the answers

Convert the binary number 1011011 to hexadecimal.

<p>0x5B (D)</p> Signup and view all the answers

What is the binary representation of the hexadecimal number 0xA5?

<p>10100101 (D)</p> Signup and view all the answers

What is the decimal equivalent of the binary number 11010011?

<p>211 (A)</p> Signup and view all the answers

Which of these binary numbers is equivalent to the hexadecimal number 0xCE?

<p>11001110 (A)</p> Signup and view all the answers

What is the decimal equivalent of 0xAF?

<p>175 (C)</p> Signup and view all the answers

In the context of binary multiplication, what is the purpose of shifting the result one bit to the right?

<p>To maintain the correct positional value of the bits in the product. (D)</p> Signup and view all the answers

Which of the following statements accurately describes the role of a nibble in binary representation?

<p>A nibble is a 4-bit unit that can represent 16 different states of information. (B)</p> Signup and view all the answers

How many unique states can be represented by a string of 8 bits?

<p>256 (C)</p> Signup and view all the answers

From the binary number 111011001010, what is the decimal value of the leftmost 4 bits?

<p>14 (B)</p> Signup and view all the answers

What is the hexadecimal representation of the binary number 1010011001?

<p>0x269 (C)</p> Signup and view all the answers

Which of the following number bases is NOT commonly used to represent data in a computer system?

<p>Base 8 (octal) (D)</p> Signup and view all the answers

In the binary multiplication example provided, what is the decimal equivalent of the product (101101 x 10101)?

<p>1099931 (A)</p> Signup and view all the answers

Why is the base of a number system important in computer science?

<p>It determines the number of unique characters used to represent information. (A)</p> Signup and view all the answers

What is the largest decimal number that can be represented using a nibble?

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

Which of the following is the most common representation for storing data in modern computers?

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

What is a necessary condition for establishing an internet connection?

<p>A powerful computer machine (B)</p> Signup and view all the answers

Which of the following accurately defines the function of an ISP?

<p>It provides internet services to users. (C)</p> Signup and view all the answers

How many computers were estimated to be on the internet by the end of 1992?

<p>Over 1 million (B)</p> Signup and view all the answers

Which characteristic is true about a web page?

<p>It must have hyperlinks to enhance interactivity. (C)</p> Signup and view all the answers

Which of the following is not a requirement for accessing the internet?

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

Which OSI layer is responsible for error detection during node-to-node transmission?

<p>Data Link Layer (D)</p> Signup and view all the answers

What function does the Presentation Layer NOT perform?

<p>Interface between various network devices (C)</p> Signup and view all the answers

Which layer of the OSI model would manage end-to-end flow control?

<p>Transport Layer (C)</p> Signup and view all the answers

How does the Network Layer primarily assist in data transmission?

<p>By assigning addresses and routing packets (C)</p> Signup and view all the answers

Which OSI layer is concerned with the physical interface of network hardware?

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

What function does the sign bit serve in binary floating-point representation?

<p>It indicates whether the number is positive or negative. (A)</p> Signup and view all the answers

In the provided example, how many bits are allocated to the mantissa in an 8-bit floating-point system?

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

Which of the following describes truncation error in floating-point representation?

<p>Error arising from the limited precision of the floating-point representation. (C)</p> Signup and view all the answers

What is the decimal equivalent of the binary notation represented by the bits 101.1101?

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

What segments does the notation 01011101 break into in a floating-point system?

<p>Sign Bit: 0, Exponent: 101, Mantissa: 1101 (B)</p> Signup and view all the answers

Which base is NOT commonly associated with representing data in computer systems?

<p>Base 12 (D)</p> Signup and view all the answers

What is the effect of increasing the number of bits for the mantissa field?

<p>Reduces the potential for truncation errors. (A)</p> Signup and view all the answers

In the context of floating-point representation, what is the primary role of the exponent?

<p>To scale the value of the mantissa. (C)</p> Signup and view all the answers

What issue arises from using only 8 bits for floating-point representation?

<p>Increased likelihood of round-off errors. (A)</p> Signup and view all the answers

What is the result of adding the binary numbers 10110010 and 11010111?

<p>110101001 (B)</p> Signup and view all the answers

Which of the following statements about binary subtraction is true?

<p>The 2's complement of the number being subtracted is added. (A)</p> Signup and view all the answers

When 1 is added to 1 in binary addition, what is the result and what is the carry?

<p>0 with carry 1 (A)</p> Signup and view all the answers

What will the 2's complement of the binary number 1101 be?

<p>0011 (D)</p> Signup and view all the answers

What is achieved by ignoring the overflow bit in binary addition?

<p>It ensures every sum remains a 4-bit number. (A)</p> Signup and view all the answers

What does flipping all the bits of a binary number result in before calculating the 2's complement?

<p>Obtaining the 1's complement. (C)</p> Signup and view all the answers

What binary number represents the decimal value 3 when using the binary subtraction of 1100 minus 1001?

<p>0011 (C)</p> Signup and view all the answers

In the example of adding 11001 and the 2's complement of 01110, what does the padded bit allow for?

<p>It equalizes the length of the binary numbers. (B)</p> Signup and view all the answers

Which of these options correctly describes how a carry is handled during binary addition?

<p>Carried to the next left column. (D)</p> Signup and view all the answers

A computer processes data in batches. What is the unit of data that a computer processes at a time called?

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

What is the significance of a byte in the context of representing information?

<p>A byte is used to represent a single character in most languages. (B)</p> Signup and view all the answers

Why is feeding just 8 bits (1 byte) to a computer to process at a time considered a waste of processing power?

<p>Because a computer can process a larger number of bits at a time, and feeding only 8 bits underutilizes its capabilities. (C)</p> Signup and view all the answers

Imagine a string of bits representing information. What would determine the duration of each bit in this string?

<p>The duration of the electrical pulse used to represent the bit. (A)</p> Signup and view all the answers

What does the voltage difference between the 0 and the 1 states of a bit represent?

<p>The distinction or contrast that defines the two states. (C)</p> Signup and view all the answers

The text mentions that the duration of each bit in a string depends on the duration of the pulse. What does this imply about the representation of information?

<p>The duration of the pulse influences how long the information remains valid or active. (C)</p> Signup and view all the answers

Why is the number of bits essential for conveying information?

<p>Each bit can be in one of two states (0 or 1), so the increasing number of bits allows for a greater number of possible combinations, thus representing more diverse information. (A)</p> Signup and view all the answers

What is the maximum decimal value represented by a nibble in binary?

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

How many unique values can a string of 4 bits represent?

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

In binary multiplication, what is the significance of shifting the result one bit to the right?

<p>It aligns the result to the next place value. (B)</p> Signup and view all the answers

What represents the decimal equivalent of the binary value 1010?

<p>10 (D)</p> Signup and view all the answers

What effect does multiplying any binary number by 0 have?

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

During binary multiplication, how is the product of each step summed together?

<p>By performing binary addition. (B)</p> Signup and view all the answers

Which of the following correctly describes a binary digit?

<p>The smallest unit of data in a binary system. (C)</p> Signup and view all the answers

In the binary example provided of multiplying 101101 by 10101, what is the final result?

<p>1110110001 (C)</p> Signup and view all the answers

What is the primary purpose of the base in a number system?

<p>To define the total number of unique symbols. (A)</p> Signup and view all the answers

At what power of 2 does a nibble (4 bits) allow representation of unique states?

<p>2^4 (A)</p> Signup and view all the answers

Flashcards

Binary Addition with Carry

When adding binary numbers, if there is a carry, add it to the least significant bit.

Overflow Bit

The leftmost bit that indicates overflow in binary addition is ignored.

1's Complement

The 1's complement of a binary number is obtained by flipping all bits.

Finding Negative Result

To find a negative result, take the 1's complement and add a negative sign.

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Division of Bits

Division in binary is done through repeated subtraction of the divisor from the dividend.

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Borrow in Division

A borrow occurs when the divisor exceeds the dividend during subtraction.

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Binary Multiplication

Binary multiplication is completed through series of shifts and additions.

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Binary Digit (Bit)

The smallest unit of data in computing, representing 0 or 1.

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Base Two Number

A number represented in binary format using two digits: 0 and 1.

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Nibble

A group of four bits, which can represent 16 different values.

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Decimal Equivalent

The base 10 representation of binary values.

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Hexadecimal

A base 16 number system using digits 0-9 and letters A-F.

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States in Binary

The possible values that a binary number can represent: 0 or 1.

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Bitwise Multiplication

A step-by-step method of binary multiplication using individual bits.

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2 raised to the power of n

The formula to determine how many different states 'n' bits can represent.

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Binary conversion

The process of converting a decimal number to binary format.

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Remainders

The left-over amount after division, important for binary conversion.

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Hexadecimal numbers

Numbering system using base 16, combining digits and letters.

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Hexadecimal State

The position of a number in the hexadecimal system from 0 to F.

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Binary Equivalent

The representation of a number in binary format (base 2).

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0x prefix

A notation indicating a number is in hexadecimal format.

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Convert binary to hex

The method of grouping binary bits and translating them to hexadecimal.

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Decimal numbering

The system where each digit has a position based on powers of 10.

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Conversion steps

Sequential procedures to translate between number systems, e.g., binary to hex.

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Internet Growth

The internet connected networks globally, exceeding a billion users.

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ISP

Internet Service Provider; a company providing internet access.

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WWW

World Wide Web; a system to access information online.

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E-Mail

Electronic mail; a method to send messages digitally.

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Basic Requirements for Internet

Essentials include a computer, OS, RAM, modem, ISP, and more.

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Hexadecimal Conversion

The process of converting decimal numbers to hexadecimal by dividing by 16.

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Decimal to Hex Example

734593 in decimal converts to 0xB3581 in hexadecimal.

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Integers

Whole numbers that can be positive, negative, or zero, represented as set Z.

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Set Z Definition

The set of integers includes {..., -3, -2, -1, 0, 1, 2, 3, ...}.

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Two's Complement Notation

A method to represent negative integers in binary form using fixed bits.

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Range of Integers

Determined by the number of bits used in two's complement notation.

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Obtaining Two's Complement

Flip bits of positive binary, then add 1 to the least significant bit.

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Sign Bit

The leftmost bit indicates if an integer is positive (0) or negative (1).

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32-bit Integers

Modern computers typically use 32 bits to represent integers in binary.

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Remainders in Hex Conversion

In decimal to hex conversion, remainders are recorded from last to first.

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Bit

The smallest unit of data, representing two states: 0 or 1.

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Byte

A grouping of 8 bits used to represent data, like characters in languages.

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Word

The number of bits a computer can process at once, varies by architecture.

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Voltage Levels in Bits

The difference between representing 0 (OFF) and 1 (ON) in electrical terms.

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Pulse Duration

The time a bit is held in its state, affecting how information is processed.

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Binary Digit

The formal term for a bit, used in computing and data processing.

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Information Processing

The manipulation of bits to convert raw data into useful information.

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OSI Model Layers

The OSI model consists of seven layers that standardize networking protocols.

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Physical Layer

This layer deals with the physical hardware and transmission media in networking.

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Transport Layer

It ensures reliable data transfer between devices, managing error and flow control.

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Session Layer

This layer maintains connections and sessions between applications, handling authentication.

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Application Layer

This layer allows applications to communicate over a network using protocols like HTTP.

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Binary Multiplication Steps

The process of multiplying binary numbers through shifting and adding results based on each bit.

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Floating Point Notation

A method to represent real numbers using a sign bit, exponent, and mantissa.

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Result of Binary Multiplication

The sum of all the shifted results from binary multiplication.

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Base of Number Systems

Refers to the number of unique digits used to represent numbers in a system.

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Exponent

The part of the floating point that represents the value greater than one.

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Mantissa

The part of the floating point representing values less than one.

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Truncation Error

Errors that occur due to limited bits used for mantissa and exponent.

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Binary States

The possible values a binary number can have, which are 0 and 1.

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Binary Breakdown

Dividing a binary stream into sign, exponent, and mantissa segments.

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Decimal Equivalent of Binary

The base 10 representation of binary values; how binary translates to decimal.

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Decimal Equivalent Calculation

The process of converting a binary number into decimal form.

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8-Bit System

A binary system where 8 bits are used to represent numbers, divided into sign, exponent, and mantissa.

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Power of 2 in Bits

2^n represents how many unique states n bits can represent.

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Binary String Example

A sequence of bits, such as 0001, representing specific information or values.

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Power of Base

The expression that allows interpretation of binary numbers in decimal format.

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Base Systems

Different numeral systems, such as binary (base 2), decimal (base 10), and hexadecimal (base 16).

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Bit vs Byte

A byte consists of 8 bits, while a bit is a single binary digit.

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Binary Addition

The process of adding binary numbers column by column, treating 2 as a carry to the next column.

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Adding Bits with Carry

When bits add up to 2, write down 0 and carry 1 to the next left column.

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Binary Subtraction

Subtraction in binary is performed by adding the 2's complement of the subtracted number.

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Two's Complement

A method to find the subtraction result by flipping bits and adding 1 for negative values.

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Carrying in Binary

A carry occurs when the sum exceeds the base (2), similarly like in decimal addition.

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Structure of Binary Addition

Align binary numbers to the right before adding for accurate results.

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Borrow in Binary Subtraction

When subtracting, a borrow occurs when the top bit is smaller than the bottom bit.

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Overflow Bit in Addition

An overflow bit is ignored when adding binary numbers if it exceeds the designated bits.

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Sum of Binary Numbers

The result of adding two or more binary values together following binary addition rules.

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Study Notes

Module 4: Machine Level Representation of Data

  • Data is processed by computers into information
  • Data is unorganized, raw form
  • Fundamental operations are performed on the smallest unit of data, the bit
  • Bits are binary digits, represented as 0 and 1
  • 0 represents OFF/LOW; 1 represents ON/HIGH
  • Bit duration and voltage difference are important factors
  • A group of 8 bits is a byte (represented by 'B')
  • Computers process large amounts of data at once, processing in batches
  • Word length refers to the number of bits a computer can process simultaneously
  • Units of information (kilobits, megabits, gigabits, terabits, kilobytes, megabytes, gigabytes, terabytes) are used
    • Table 1 provides conversions between units
  • One kilobyte equals 1024 bytes
  • One megabyte equals 1,048,576 bytes
  • One gigabyte equals 1,073,741,824 bytes
  • One terabyte equals 1,099,511,627,776 bytes
  • Bits are used to represent various characters in most languages
  • Example 1: Figure showing a string of bits 10110
  • Example 2 showing one byte: 10110010

Addition of Bits

  • Steps for binary addition are similar to decimal addition
    • Align bits to be added
    • Start adding the bits in the far right column
    • Use the rule (1+0 = 1, 0 + 0 = 0, 1+1 = 0 add 1 to the next column)
  • Example 5: Binary addition of 100100102 and 110101112 to find carry bit -Carry bit of 111 is added to least significant bits

Subtraction of Bits

  • 2's complement is used for subtraction
    • Turn all 0s to 1s and all 1s to 0s
    • Add 1 to the last bit on the right

Division of Bits

  • A series of subtractions using the divisor and the dividend
  • Remainder is added to the remaining bits in order to find the quotient
  • Example: find 01111100 / 0010, which gives a remainder of 00

Multiplication of Bits

  • Achieved through shifting and addition
  • Steps are involved in the process
  • Example: Multiply 101101 x 10101 = 1110110001

Number Bases and Types

  • Binary numbers exist in two states (0 and 1)
  • Each bit is called a numeral, sequence of bits provides data that has more than two states
  • Decimal numbers use 10 possible numbers or numerals
  • Hexadecimal numbers use 16 possible numbers or numerals
  • Example: Convert 11001010 to a decimal which is 202
  • Example: Convert 73459310 = 0xB3581

Representation of Non-Numeric Data, Records, and Registers

  • Non-numeric data includes alphabets, symbols, images, and audio.
  • Coded formats are used to represent non-numeric data
  • ASCII (American Standard Code for Information Interchange) is frequently used and represents letters, numbers and other special characters in binary code.
  • Example: What will be the ASCII code (in binary) to represent CODEL!
    • The codes are 1000011,1001111,1000100, 1100101, 1101100, 0100001 respectively

Computer Records and Registers

  • A record combines various data objects
  • Registers are small memory blocks
  • They speed up operations by providing quick access to commonly used values.
  • Registers store data temporarily
  • Examples of registers include Accumulator (AC), Data Register (DR), Instruction Register(IR), Address Register(AR), Program Counter(PC), Input Register(INPR), and Output Register(OUTR).
  • TR: Temporary Register - 16 bits.
  • IR: Instruction Register - 16 bits.
  • AR: Address Register - 12 bits
  • PC: Program Counter - 12 bits.
  • INPR: Input Register - 8 bits.
  • OUTR: Output Register - 8 bits.

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Description

This quiz covers the essentials of machine-level representation of data, focusing on bits, bytes, and their operations. Understand how data is organized and the significance of various units used in computing. Explore the fundamental concepts of data processing and storage in computer systems.

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