Number Systems

Question 1

Why must data be converted to binary to be processed by a computer?

Answer 1

Data has to be converted to binary to be processed by a computer because computers are built using switches that can either be on or off, which fits the binary number system (1/0).

Question 2

Define binary data.

Answer 2

Binary data is data represented using the binary number system, consisting of only two digits: 1 and 0.

Question 3

Define binary number system.

Answer 3

The binary number system is a base-2 number system that represents numbers using only two digits: 0 and 1.

Question 4

What is the advantage of processing data in binary format for computers? (3)

Answer 4

allows computers to perform:

• complex calculations
• store vast amounts of data efficiently
• operate at incredible speeds.

Question 5

What is denary?

Answer 5

Denary is a base-10 number system made up of 10 digits (0-9), where each digit has a weight factor of 10 raised to a power.

Question 6

What is hexadecimal?

Answer 6

Hexadecimal is a base-16 number system made up of 16 digits, including 10 numbers (0-9) and 6 letters (A-F).

Question 7

How many unique values can one hexadecimal digit represent?

Answer 7

16 unique values (0-F).

Question 8

What is the largest decimal number that can be represented by 8 bits in binary?

Answer 8

255 (11111111 in binary)

Question 9

How many bits does one hexadecimal digit represent?

Answer 9

4 bits (half a byte or one nibble)

Question 10

Define nibble.

Answer 10

A nibble is four bits of binary data or half a byte.

Question 11

Define byte.

Answer 11

A byte is a unit of digital information that consists of 8 bits.

Question 12

What is the definition of bit?

Answer 12

A bit is a basic unit of information in computing, representing either a 0 or 1.

Question 13

Why is hexadecimal preferred when working with large values in Computer Science?

Answer 13

Hexadecimal is preferred because:

• it takes fewer digits to represent a given value than binary making it easier to read
• less prone to errors when copying.

Question 14

Define MAC address.

Answer 14

A unique identifier for network interfaces, typically consisting of 12 hexadecimal digits which is equivalent to 48 digits in binary.

Question 15

What is the format of a typical hexadecimal color code?

Answer 15

A typical hexadecimal color code consists of 6 hexadecimal digits, equivalent to 24 digits in binary. Each two-digit pair represents the colors red, green, and blue

Question 16

Define URL encoding.

Answer 16

The process of converting characters in a URL that are outside the standard set into hexadecimal codes.

Question 17

What are three common uses of hexadecimal in computing?

Answer 17

• MAC addresses
• URL encoding
• Color codes

Question 18

Define overflow error.

Answer 18

An overflow error occurs when a result is too large to be represented in the available storage space (needs more bits)

Question 19

What is 1 + 1 in binary addition?

Answer 19

1 + 1 = 10 (2 in denary)

Question 20

Define binary shift.

Answer 20

A binary shift is how a computer system performs basic multiplication and division by moving binary digits left or right a set number of times.

Question 21

What does a left shift do?

Answer 21

A left shift multiplies a binary number by 2 (for every 1 place shift).

Question 22

What does a right shift do?

Answer 22

A right shift divides a binary number by 2 (for every 1 place shift).

Question 23

Define underflow error.

Answer 23

An underflow error occurs when a result is too small to be represented in the available storage space.

Question 24

In binary shifts, what is the definition of precision?

Answer 24

In binary shifts, precision refers to the number of digits used to represent a value.

Question 25

Define Two’s complement.

Answer 25

A method of using signed binary values to represent negative numbers, where the leftmost bit is designated as the most significant bit (MSB).

Question 26

How is a negative number represented in two’s complement?

Answer 26

In two’s complement, a negative number is represented by setting the most significant bit (MSB) to 1.

Question 27

Define MSB.

Answer 27

The Most Significant Bit, which in two’s complement represents the sign of the number (0 for positive, 1 for negative).

Question 28

State one effect this logical shift has on the binary number

Answer 28

• Value becomes incorrect

Question 29

Give two reasons why a programmer may use hexadecimal to represent binary numbers

Answer 29

• Shorter representation
• Easier to write