Binary Conversion Steps for Decimal Number

Questions and Answers

What is the binary equivalent of the decimal number 2910?

1010101100

1110011010 (correct)

11100110110

1111001110

Which step in calculating the decimal from binary involves multiplying column values by digits?

Step 4

Step 3

Step 1

Step 2 (correct)

What is the significance of the order of remainders in binary conversion?

The last remainder represents the Least Significant Digit. (correct)

Remainders should be arranged random to check accuracy.

The order does not affect the final result.

The first remainder is the Most Significant Digit.

What is the result of summing the products of the binary number 111012 when calculated in decimal form?

2910 Signup and view all the answers

What is the first step when converting a number from another base to a non-decimal system?

Convert the original number to a decimal number. Signup and view all the answers

What is the decimal equivalent of the octal number 258?

211 Signup and view all the answers

What is the binary equivalent of the octal number 258?

101012 Signup and view all the answers

When converting binary to octal, what is the first step?

Divide binary digits into groups of three Signup and view all the answers

In converting octal 258 to binary, what is the binary representation of the octal digit 5?

101 Signup and view all the answers

What is the last binary digit when converting the decimal number 21 to binary?

1 Signup and view all the answers

Which step is incorrect when converting binary 101012 into octal?

Grouping into pairs instead of threes Signup and view all the answers

During the conversion of the decimal number 21 into binary, what is the second step?

10 / 2 gives 5 Signup and view all the answers

What is the binary representation of the octal digit 2 in the conversion from octal to binary?

010 Signup and view all the answers

What is the correct hexadecimal equivalent of the binary number 101012?

1516 Signup and view all the answers

Which of the following accurately describes the function of a half-adder?

It requires two binary inputs and produces a sum and carry. Signup and view all the answers

What characterizes a combinational circuit?

It depends only on the current input for its output. Signup and view all the answers

Which step is NOT part of the conversion from hexadecimal to binary?

Performing arithmetic addition on the hexadecimal values. Signup and view all the answers

What is the output of a half-adder when the inputs are both 1?

Sum = 1, Carry = 1 Signup and view all the answers

Which of the following is NOT a type of combinational logic circuit?

Flip-flop Signup and view all the answers

What is the first step in converting a hexadecimal number to binary?

Convert each hexadecimal digit to a 4-digit binary number. Signup and view all the answers

Which of the following best describes a full adder compared to a half adder?

A full adder can add three binary digits. Signup and view all the answers

What does the execution unit (EU) do in the 8086 architecture?

Translates instructions into actions Signup and view all the answers

Which of the following components are part of the execution unit (EU)?

General purpose registers and flag register Signup and view all the answers

What is the primary function of a half-adder?

To add two binary numbers and generate carry output. Signup and view all the answers

What is the primary function of the bus interface unit (BIU) in the 8086 architecture?

Manage data and address transfer Signup and view all the answers

How does the architecture of the 8086 support pipelining?

By allowing the execution unit and bus interface unit to work simultaneously Signup and view all the answers

What is the main difference between a half-adder and a full-adder?

Half-adder has two inputs and produces two outputs, while full-adder has three inputs and two outputs. Signup and view all the answers

In the context of the 8086 architecture, what does the instruction decoder do?

Translates instructions into a series of actions Signup and view all the answers

Which logical operation does the sum output of a half-adder represent?

XOR operation of the two inputs. Signup and view all the answers

How many NAND/NOR gates are required for implementing a full-adder?

9 gates. Signup and view all the answers

What type of data can the general purpose registers in the execution unit store?

Temporary data during execution Signup and view all the answers

Which statement accurately describes how the EU and BIU function together?

EU handles instruction execution while BIU manages instruction fetching Signup and view all the answers

What does the carry output of a half-adder indicate?

The sum of A and B exceeds the value of 1. Signup and view all the answers

Which register in the execution unit is primarily responsible for directing internal operations?

Control circuitry Signup and view all the answers

Which device is responsible for accepting coded information as the source program in a computer?

Input device. Signup and view all the answers

What new functionality does a full-adder provide compared to a half-adder?

Adding three binary digits including a carry input. Signup and view all the answers

What role does the memory play in a computer system?

To store programs and temporary data. Signup and view all the answers

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.