3.2

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Questions and Answers

How are computer words represented in binary?

Computer words are composed of bits, which can represent numbers in binary form.

What is the role of carries in binary addition?

Carries in binary addition are used to pass values from one digit to the next, ensuring accurate sums.

In binary subtraction, how is the operation performed?

Binary subtraction is performed by negating the appropriate operand and adding it to the first operand.

Why might arithmetic operations create numbers that cannot be represented?

Certain arithmetic operations may result in numbers larger than the maximum representable value in a given binary format. Signup and view all the answers

What are the implications of arithmetic algorithms for instruction sets?

Arithmetic algorithms inform how instruction sets are designed to efficiently perform operations on numbers. Signup and view all the answers

What is the condition that indicates overflow when adding two positive numbers?

Overflow occurs when the sum is negative. Signup and view all the answers

How can one detect overflow in subtraction operations?

Overflow occurs if a negative result arises from subtracting a negative number from a positive one, or vice versa. Signup and view all the answers

Why is overflow particularly significant when dealing with 32-bit numbers?

Because adding or subtracting them can yield results requiring 33 bits to express fully. Signup and view all the answers

What does the Arithmetic Logic Unit (ALU) check for in unsigned integers?

The ALU checks for overflow by verifying if the sum is less than either of the addends. Signup and view all the answers

Describe a scenario where subtraction results in overflow in unsigned integers.

Overflow happens if the difference is greater than the minuend. Signup and view all the answers

What is the result of adding the binary numbers `00000000 00000000 00000000 00000111two` and `11111111 11111111 11111111 11111010two`?

The result is <code>00000000 00000000 00000000 00000001two</code>, which equals 1 in decimal. Signup and view all the answers

When can overflow occur in binary addition?

Overflow can occur when adding two operands with the same sign, specifically when both are positive or both are negative. Signup and view all the answers

Explain how subtraction can be performed using binary addition and two's complement.

Subtraction can be performed by negating the second operand and adding it to the first operand, using its two's complement representation. Signup and view all the answers

Why can overflow not occur when adding operands with different signs?

When adding operands with different signs, the result must fit within the range of one of the operands, preventing overflow. Signup and view all the answers

What does the carry out from a binary addition operation signify?

The carry out signifies that the result of that bit addition exceeded the maximum value for that bit and must be carried over to the next higher bit. Signup and view all the answers

Study Notes

Introduction

Computer words are made up of bits and can be written as binary numbers
Computers can represent integers in decimal or binary form
There are other forms besides integers that need to be considered:
- Fractions
- Real numbers
- Overflow conditions
Hardware multiplication and division are complex

Addition and Subtraction

Computers perform addition in the same way as humans: digit by digit from right to left, with carries passed to the left
Subtraction is performed using addition by negating the operand before performing addition
An overflow occurs when the result of a calculation is too large to be represented by the available hardware
Overflow can only occur during addition when adding operands of the same sign
Overflow can be detected during addition in two's complement representation by checking if the sign bit is set incorrectly
Overflow cannot occur when adding operands of different signs
Overflow can also be detected with unsigned integers
The Arithmetic Logic Unit (ALU) is the hardware component that performs addition, subtraction, and logical operations

Multiplication

Multiplication within computers is done by a series of additions
Multiplication of binary numbers is similar to the longhand multiplication of decimal numbers
The speed of addition can be improved by anticipating the carry bit using carry lookahead
Saturation arithmetic is a feature not generally found in general-purpose microprocessors
Saturation arithmetic ensures that the result of an operation is limited to the maximum or minimum value if an overflow occurs
This type of arithmetic is useful in media applications to prevent abrupt volume changes, for example

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Description

This quiz covers the fundamentals of computer arithmetic, including binary representation of numbers, addition and subtraction methods, and the concept of overflow in calculations. Understand how computers handle fractions and real numbers in arithmetic operations, along with the complexities involved in hardware multiplication and division.

3.2

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