2. Data Representation

Flashcards based on lecture material. Made by Gemini 2.5 Pro.

What is the most basic unit of information in a digital computer?

A bit (binary digit).

How many bits are in a byte?

8 bits.

A group of 4 bits is also known as a…?

Nibble.

What is the natural unit of data used by a particular processor design, typically 32 or 64 bits in modern computers?

A word.

What is the binary representation of the decimal number 21?

10101

What is the binary representation of the decimal number 74?

1001010

What is the binary representation of the decimal number 234?

11101010

What is the decimal equivalent of the unsigned binary number 10010101?

149

What is the largest unsigned number that can be stored in a 4-bit word?

15 (2⁴ - 1)

What is the largest unsigned number that can be stored in an 8-bit word?

255 (2⁸ - 1)

What is the largest unsigned number that can be stored in a 16-bit word?

65,535 (2¹⁶ - 1)

What is the largest unsigned number that can be stored in a 32-bit word?

4,294,967,295 (2³² - 1)

What is the one's complement of the binary number 10101100?

1010011

What is the one's complement of the binary number 01010100?

10101011

In 2's complement, what is the range of numbers that can be stored in a 3-bit word?

-4 to 3

In 2's complement, what is the range of numbers that can be stored in a 4-bit word?

-8 to 7

In 2's complement, what is the range of numbers that can be stored in an 8-bit word?

-128 to 127

How do you find the negative of a number using two's complement arithmetic?

Invert all the bits (one's complement) and then add 1.

What is the negative of the binary number 01010011 using 2's complement?

10101101

What is the decimal equivalent of the 5-bit two's complement number 00011?

3

What is the decimal equivalent of the 5-bit two's complement number 01111?

15

What is the decimal equivalent of the 5-bit two's complement number 11100?

-4

What is the decimal equivalent of the 5-bit two's complement number 11010?

-6

What is the decimal equivalent of the 5-bit two's complement number 10000?

-16

What is the 8-bit two's complement representation of the decimal number 12?

1100

What is the 8-bit two's complement representation of the decimal number -15?

11110001

What is the 8-bit two's complement representation of the decimal number -117?

10001011

The hexadecimal number C6 is used to represent a two's complement binary number. What is its decimal value?

-58

Can the addition of two negative numbers (e.g., 1??? + 1???) in 2's Complement produce an overflow?

Yes, if the result appears to be positive (i.e., the sign bit becomes 0).

Can subtracting a positive number from another positive number (e.g., 0??? - 0???) in 2's Complement produce an overflow?

No. This is treated as adding a positive and a negative, which can never cause an overflow.

What is the numerical value of the Least Significant Bit (LSB) when it is set to 1?

1 (representing 2⁰)

What is the binary representation of the hexadecimal number BC?

10111100

What is the binary representation of the hexadecimal number F0?

11110000

What is the decimal equivalent of the hexadecimal number 3F?

63

Express the binary number 101010101010 in hexadecimal notation.

AAA

Express the binary number 110010110111 in hexadecimal notation.

CB7

What is the octal representation of the decimal number 37?

45

What is the octal representation of the decimal number 89?

131

What is the result of adding the unsigned binary numbers 01010101 + 00111111?

10010100

What is the term for when the result of an arithmetic operation is too large to be represented by the available number of bits?

Overflow.

In this storage system, the most significant byte is stored at the lowest memory address.

Big-Endian.

In this storage system, the least significant byte is stored at the lowest memory address.

Little-Endian.

What is the primary advantage of using two's complement for representing signed integers in computers?

It simplifies arithmetic operations, allowing subtraction to be performed via addition.

In signed-magnitude representation, what is a significant disadvantage related to the number zero?

There are two representations for zero (+0 and -0), which complicates logic and wastes a bit pattern.

How are real numbers (including fractions and very large/small numbers) typically represented in computers?

Floating-Point Representation (a form of scientific notation).

What are the three components of a floating-point number?

Sign, Mantissa (or Significand), and Exponent.

This character encoding standard includes representations for characters from almost all of the world's writing systems.

Unicode.

The rule of thumb for detecting overflow in a signed 2's complement addition is when the 'carry in' to the sign bit is … from the 'carry out'.

different

Each digit in the hexadecimal (base-16) system represents how many binary bits?

4 bits.

Each digit in the octal (base-8) system represents how many binary bits?

3 bits.