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Questions and Answers
What is the binary equivalent of the decimal number 2910?
What is the binary equivalent of the decimal number 2910?
Which step in calculating the decimal from binary involves multiplying column values by digits?
Which step in calculating the decimal from binary involves multiplying column values by digits?
What is the significance of the order of remainders in binary conversion?
What is the significance of the order of remainders in binary conversion?
What is the result of summing the products of the binary number 111012 when calculated in decimal form?
What is the result of summing the products of the binary number 111012 when calculated in decimal form?
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What is the first step when converting a number from another base to a non-decimal system?
What is the first step when converting a number from another base to a non-decimal system?
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What is the decimal equivalent of the octal number 258?
What is the decimal equivalent of the octal number 258?
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What is the binary equivalent of the octal number 258?
What is the binary equivalent of the octal number 258?
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When converting binary to octal, what is the first step?
When converting binary to octal, what is the first step?
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In converting octal 258 to binary, what is the binary representation of the octal digit 5?
In converting octal 258 to binary, what is the binary representation of the octal digit 5?
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What is the last binary digit when converting the decimal number 21 to binary?
What is the last binary digit when converting the decimal number 21 to binary?
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Which step is incorrect when converting binary 101012 into octal?
Which step is incorrect when converting binary 101012 into octal?
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During the conversion of the decimal number 21 into binary, what is the second step?
During the conversion of the decimal number 21 into binary, what is the second step?
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What is the binary representation of the octal digit 2 in the conversion from octal to binary?
What is the binary representation of the octal digit 2 in the conversion from octal to binary?
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What is the correct hexadecimal equivalent of the binary number 101012?
What is the correct hexadecimal equivalent of the binary number 101012?
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Which of the following accurately describes the function of a half-adder?
Which of the following accurately describes the function of a half-adder?
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What characterizes a combinational circuit?
What characterizes a combinational circuit?
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Which step is NOT part of the conversion from hexadecimal to binary?
Which step is NOT part of the conversion from hexadecimal to binary?
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What is the output of a half-adder when the inputs are both 1?
What is the output of a half-adder when the inputs are both 1?
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Which of the following is NOT a type of combinational logic circuit?
Which of the following is NOT a type of combinational logic circuit?
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What is the first step in converting a hexadecimal number to binary?
What is the first step in converting a hexadecimal number to binary?
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Which of the following best describes a full adder compared to a half adder?
Which of the following best describes a full adder compared to a half adder?
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What does the execution unit (EU) do in the 8086 architecture?
What does the execution unit (EU) do in the 8086 architecture?
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Which of the following components are part of the execution unit (EU)?
Which of the following components are part of the execution unit (EU)?
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What is the primary function of a half-adder?
What is the primary function of a half-adder?
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What is the primary function of the bus interface unit (BIU) in the 8086 architecture?
What is the primary function of the bus interface unit (BIU) in the 8086 architecture?
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How does the architecture of the 8086 support pipelining?
How does the architecture of the 8086 support pipelining?
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What is the main difference between a half-adder and a full-adder?
What is the main difference between a half-adder and a full-adder?
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In the context of the 8086 architecture, what does the instruction decoder do?
In the context of the 8086 architecture, what does the instruction decoder do?
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Which logical operation does the sum output of a half-adder represent?
Which logical operation does the sum output of a half-adder represent?
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How many NAND/NOR gates are required for implementing a full-adder?
How many NAND/NOR gates are required for implementing a full-adder?
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What type of data can the general purpose registers in the execution unit store?
What type of data can the general purpose registers in the execution unit store?
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Which statement accurately describes how the EU and BIU function together?
Which statement accurately describes how the EU and BIU function together?
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What does the carry output of a half-adder indicate?
What does the carry output of a half-adder indicate?
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Which register in the execution unit is primarily responsible for directing internal operations?
Which register in the execution unit is primarily responsible for directing internal operations?
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Which device is responsible for accepting coded information as the source program in a computer?
Which device is responsible for accepting coded information as the source program in a computer?
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What new functionality does a full-adder provide compared to a half-adder?
What new functionality does a full-adder provide compared to a half-adder?
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What role does the memory play in a computer system?
What role does the memory play in a computer system?
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Study Notes
Number System Conversions
- Decimal number 2910 converts to binary 111012 through successive division by 2, yielding remainders of 1, 0, 1, 1, and 1.
- The process for converting binary 111012 back to decimal involves positional value multiplication: (1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20) equals 2910.
- Octal 258 converts to decimal by calculating ((2 × 81) + (5 × 80)), resulting in decimal 2110.
- Decimal 2110 can be converted to binary, resulting in binary 101012 using similar division steps as before.
Conversion Techniques
- Binary to octal conversion is done by grouping binary digits into sets of three (from the right) and converting each to its octal equivalent.
- Octal to binary conversion requires converting each octal digit into a three-digit binary number and combining them.
- Binary to hexadecimal involves grouping binary digits into sets of four and converting each group into a hexadecimal symbol.
- Hexadecimal to binary conversion entails converting each hexadecimal digit into a four-digit binary number.
Combinational Circuits
- Output of combinational circuits depends solely on current inputs, with no memory of previous states.
- Types of combinational circuits include adders, subtractors, decoders, encoders, multiplexers, and demultiplexers.
Half Adder
- A half-adder takes two binary inputs and provides two outputs: sum and carry.
- Logical expressions for half-adder:
- Sum = A⊕B
- Carry = AB
- Can be implemented using NAND or NOR gates.
Full Adder
- A full adder adds three 1-bit binary numbers (A, B, and C) with outputs for sum and carry.
- The main difference from a half-adder is the additional input.
- Requires two half-adders for implementation, utilizing nine universal gates (NAND/NOR).
Computer Components
- Komponents of a computer are divided into hardware (physical devices like CPU and storage) and software (programs like operating systems and applications).
- The functional units of a computer consist of input, memory, arithmetic logic unit (ALU), output, and control unit.
8086 Architecture
- 8086 architecture features a 16-bit ALU, 16-bit registers, segmented memory addressing, and overlapping instruction fetch and execution.
- Two main functional parts: Execution Unit (EU) and Bus Interface Unit (BIU) operate asynchronously, enhancing processing speed.
Execution Unit (EU)
- Informs the BIU of memory locations for instruction fetching and executes those instructions.
- Components include general purpose registers, ALU, flag register, instruction decoder, and control unit.
- Functions include fetching instruction opcodes, decoding, and performing arithmetic/logical operations.
Bus Interface Unit (BIU)
- Handles data and address transfer between the processor and memory/I/O.
- Computes addresses and fetches instruction codes, storing them in a FIFO register set known as the Queue register.
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Description
This quiz focuses on the process of converting the decimal number 29 into its binary equivalent using division by 2. Follow the steps outlined to understand how each division operation results in the final binary form. Test your understanding of binary conversion with this exercise.