Number Systems - CSE 220

These flashcards cover key concepts from the lecture on number systems, including binary, decimal, hexadecimal, conversion methods, floating-point representation, and issues related to overflow and accuracy.

What is the fundamental unit of data in digital systems?

The fundamental unit of data is the binary digit (bit).

How do we obtain the binary representation of a decimal number?

Continuously divide the number by 2 until the quotient is 0, recording the remainder; the binary number is the remainders read from last to first.

What are the weights for each column in a binary number?

Each column in a binary number has a weight of 2^i, where i is the column index starting from 0 on the right.

What is the hexadecimal representation of the binary number 10110011?

The hexadecimal representation of the binary number 10110011 is B3.

What is the method to convert a decimal number to hexadecimal?

Continuously divide the number by 16 until the quotient is 0, recording the remainder; read the remainders from last to first.

What are the potential representations for negative numbers in binary systems?

Negative numbers can be represented using sign/magnitude and two’s complement schemes.

What is the primary advantage of using two’s complement for binary representation?

It allows for binary addition and subtraction to work seamlessly between positive and negative numbers without special cases for sign.

What conditions lead to overflow in binary addition?

Overflow occurs when the result is greater than the number of available digits, and the leftmost carry is discarded.

What is the bias used in IEEE 754 single-precision format?

The bias used in IEEE 754 single-precision format is 127.

What is a significant limitation of floating-point numbers?

Many values cannot be represented accurately in floating-point format, and results of floating-point calculations are often not exact.