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Questions and Answers

What is the base system that humans commonly use to count?

Base 16

Base 8

Base 2

Base 10 (correct)

In binary representation, what do the two possible values of a bit represent?

Low and high

On and off

True and false

All of the above (correct)

What is represented by the binary number 1011 in decimal?

11 (correct)

How are binary digit positions numbered?

From the least significant bit to the most significant bit Signup and view all the answers

What is the term for a single digit in a binary number?

Bit Signup and view all the answers

What power of the base is used for the ith digit in a number representation?

base^i Signup and view all the answers

Which represents the decimal equivalent of the binary calculation (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0)?

11 Signup and view all the answers

What is the significance of the leftmost bit in a binary number?

It indicates the sign of the number in signed numbers. Signup and view all the answers

What primary issue does sign and magnitude representation face?

It results in multiple representations of zero. Signup and view all the answers

What does two's complement representation use to signify positive and negative numbers?

Leading 0s for positive, leading 1s for negative. Signup and view all the answers

What happens when an unsigned number representation attempts to subtract a larger number from a smaller number?

The binary string will display leading 1s. Signup and view all the answers

What is the maximum positive value that can be represented in 32 bits using two's complement?

2,147,483,647 Signup and view all the answers

Why was sign and magnitude representation abandoned in favor of two's complement?

It allows for easier hardware implementation. Signup and view all the answers

What is a characteristic of the two's complement representation?

It allows for a straightforward addition of numbers. Signup and view all the answers

Which of the following statements about two's complement representation is true?

It allows the representation of a range of values from $-2^{31}$ to $2^{31}-1$. Signup and view all the answers

Which flaw in sign and magnitude representation necessitated the development of two's complement?

The potential for multiple zero representations. Signup and view all the answers

What is represented by the least significant bit in an RISC-V word?

The rightmost bit Signup and view all the answers

What range of numbers can a 32-bit unsigned integer represent?

0 to 4,294,967,295 Signup and view all the answers

Why did early computers revert to using binary instead of decimal for operations?

Decimal proved inefficient for hardware design Signup and view all the answers

What happens when the result of an operation cannot be represented by the bits available in hardware?

Overflow Signup and view all the answers

Which description of the most significant bit is correct for an RISC-V word?

It represents the highest value in the 32-bit sequence Signup and view all the answers

In the binary representation of numbers, what are leading zeros typically used for?

They are usually omitted for simplicity Signup and view all the answers

What is the main reason hardware can efficiently perform arithmetic operations on binary patterns?

Binary operations align with the physical on/off states of electronics Signup and view all the answers

How is a binary number's value expressed mathematically using its bits?

As the sum of each bit multiplied by a power of two Signup and view all the answers

What is the value of the two's complement number 11111111 11111111 11111111 11111100two in decimal?

-4 Signup and view all the answers

Which bit pattern represents the most negative number in two’s complement?

1000 0000 0000 0000 0000 0000 0000 0000two Signup and view all the answers

What is a significant advantage of using two's complement representation for signed numbers?

It allows for simpler hardware design by having a single method for addition. Signup and view all the answers

What occurs when the leftmost retained bit of a two's complement binary number does not match the expected sign?

Overflow Signup and view all the answers

What happens to the sign bit in two's complement representation?

It is used to determine if the number is positive or negative. Signup and view all the answers

Which of the following describes the range of numbers represented in a 32-bit two's complement system?

From -2,147,483,648 to 2,147,483,647 Signup and view all the answers

Which of the following statements is true regarding two's complement representation?

There is only one representation for zero. Signup and view all the answers

Why was two's complement preferred over sign and magnitude representation?

It avoids complications found in both programming and hardware design. Signup and view all the answers

What is the purpose of a signed load when copying data to a register?

To copy the sign repeatedly for accurate representation Signup and view all the answers

How does the load byte unsigned (lbu) instruction handle the byte loaded?

It zero-extends to fill the register Signup and view all the answers

In what scenario are signed and unsigned loads identical?

When loading a 32-bit word into a 32-bit register Signup and view all the answers

What type of numbers do programming languages refer to as 'unsigned integers'?

Numbers that can only be positive Signup and view all the answers

What is the first step in negating a two's complement binary number?

Invert every 0 to 1 and every 1 to 0 Signup and view all the answers

How does the 'C' programming language represent both signed and unsigned integers?

Using 'int' and 'unsigned int' types Signup and view all the answers

What is the result of inverting a two's complement binary number and adding one?

It results in the negation of the original number Signup and view all the answers

What would it mean for memory addresses if they could be negative?

It would create confusion in data mapping Signup and view all the answers

Study Notes

Number Representation in Computers

Computers represent numbers using binary (base 2) rather than decimal (base 10) due to electronic signal processing.
A binary number consists of bits (binary digits), which can be either 0 or 1, corresponding to low/high or off/on signals.

Bit Numbering and RISC-V Word Structure

Bits in a 32-bit word are numbered from right to left, starting at 0 (least significant bit) to 31 (most significant bit).
RISC-V architecture allows representation of 2^32 different patterns (4,294,967,296 possibilities).

Unsigned and Signed Numbers

Unsigned numbers: Binary representations range from 0 to 2^32 - 1 (0 to 4,294,967,295).
Signed numbers: Need representation for both positive and negative values; uses two’s complement method.

Two’s Complement Representation

Two’s complement allows easy distinction between positive and negative numbers by leveraging the most significant bit (sign bit).
Positive numbers follow the same representation as unsigned numbers; negative numbers range from -1 to -2,147,483,648.
The sign bit's value indicates if a number is positive (0) or negative (1).

Conversion and Overflow

Overflow occurs when calculations yield results that cannot be represented within the designated number of bits.
In convert two's complement to decimal, invert the bits and add one to find the positive equivalent.

Memory Management and Data Types

Memory addresses start at 0 and are unsigned; programs differentiate between integers (signed) and unsigned integers (positive only).
C programming language uses "int" for signed and "unsigned int" for unsigned numbers.

Loading Data

Signed and unsigned loads handle how binary data is initially interpreted and stored in registers.
Signed load copies the sign bit into the upper bits (sign extension), while unsigned load fills upper bits with zeros.

Negating Two's Complement Numbers

Negating a two's complement number can be simplified by inverting each bit and adding one to the resulting value.
This method ensures that a number and its negated form sum to -1 (binary 111...111).

These concepts are fundamental for understanding how computers handle numerical data and make calculations.

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Description

Test your understanding of Chapter 2 on the language of computers, specifically focusing on signed and unsigned numbers. This quiz will cover how computers represent numbers in different bases, particularly binary. Enhance your knowledge of numerical representations in computer systems.

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