Math Problem Statement

The computer can tell whether an integer in memory is positive or negative by looking at the first bit. If the first bit is 0, the number is , if the first bit is 1, the number is

Solution

The computer can tell whether an integer in memory is positive or negative by looking at the first bit (also known as the sign bit in two's complement representation):

  • If the first bit is 0, the number is positive.
  • If the first bit is 1, the number is negative.

This is because of how numbers are stored in binary format using two's complement notation for signed integers.

Do you want more details or have any questions?

Here are 5 relative questions to expand this topic:

  1. What is two's complement and how does it work for negative numbers?
  2. How does the sign bit work in floating-point numbers?
  3. How does the computer perform arithmetic on signed integers?
  4. What are the limits for integer values based on bit size (e.g., 32-bit or 64-bit)?
  5. Can the same sign-bit logic apply to non-integer data types?

Tip: When working with binary numbers, the most significant bit (MSB) always plays a crucial role in determining the sign of a number in two's complement representation.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Binary Numbers
Two's Complement
Signed Integers

Formulas

Two's complement formula for negative numbers: (-x) = NOT(x) + 1

Theorems

Two's Complement Representation Theorem

Suitable Grade Level

Grades 9-12