1.4.1 - Data Types

Question 1

What is an integer?

Answer 1

An integer is a whole number. It can be positive or negative.

eg. 6, 47238, -12, 0, 15

Question 2

What is a real/float?

Answer 2

A real number is a number with a fractional part.

eg. -71.5, 5.01, -80.8, 15.0

Question 3

What is a character?

Answer 3

A single symbol used by a computer.

eg. A, Z, (, #

Question 4

What is a string?

Answer 4

A string is a collection of characters.

eg. ‘Hello, world!’, 07789

Question 5

What is a boolean value?

Answer 5

A true or false value.

Question 6

Convert the binary number 1101 into denary.

Answer 6

13

Question 7

Convert the denary value 47 into binary.

Answer 7

0010 1111

Question 8

Add these two binary numbers: 1011 and 1110.

Answer 8

11001.

Question 9

Add the two binary numbers: 0011 0011 and 1001 0110.

Answer 9

1100 1001

Question 10

Two equal (unsigned) integers, shown below, are added together. Calculate the result, showing your working. [2 marks]

00010101
00010101

Answer 10

0010 1010

Question 11

What are the two ways of expressing negative numbers in binary?

Answer 11

Sign and Magnitude.

Two’s Complement.

Question 12

How does sign and magnitude work?

Answer 12

The leftmost bit indicates the sign of the binary value.

A 0 represents a positive number and a 1 represents a negative number.

Question 13

Convert the denary number -8 into an 8-bit sign and magnitude number.

Answer 13

1000 1000

Question 14

Show a representation of denary -119 in 8-bits using sign and magnitude. [1 mark]

Answer 14

1111 0111

Question 15

How does two’s complement work?

Answer 15

The left-most significant bit is a negative number.

Question 16

How do you convert to two’s complement?

Answer 16

Flip all of the bits in the positive version of the binary number and then add one.

Question 17

Convert the denary number -8 to an 8-bit two’s complement binary number.

Answer 17

1111 1000

Question 18

Show a representation of denary -119 in 8-bits using two’s complement. [1 mark]

Answer 18

1000 1001

Question 19

Subtract 12 from 8 using two’s complement.

Answer 19

11100

Question 20

What base is hexadecimal?

Answer 20

Base 16.

Question 21

Convert the hexadecimal number A6 into denary.

Answer 21

166.

Question 22

Convert the hexadecimal number B2 into binary.

Answer 22

1011 0010.

Question 23

Convert the hexadecimal number B2 to denary.

Answer 23

178.

Question 24

Convert the 10-bit mantissa and 6-bit two’s complement number into denary.

1100 1001 11 0001 01

Answer 24

50.4375

Question 25

A computer represents floating point binary numbers using a 6-bit mantissa and a 4-bit exponent, both using two's complement. Add the following three numbers together and give the answer in the format described. [6 marks] 010100 0010 011000 0001 100010 0010

Answer 25

010000 1111

Question 26

What does normalising a floating-point binary number allow for?

Answer 26

It makes sure the number is as precise as possible.

Question 27

What does a normalised positive floating-point binary number start with?

Answer 27

01

Question 28

What does a normalised negative floating-point binary number start with?

Answer 28

10

Question 29

Normalise the following binary number. 000110100101 0101

Answer 29

0110 1000 0011

Question 30

What must be the same to add floating-point binary numbers?

Answer 30

Their exponents.

Question 31

Add the following floating-point numbers. 000100 0011 000101 0010

Answer 31

011010 0001

Question 32

What is a shift used for in the manipulation of binary?

Answer 32

To multiply or divide a number.

Question 33

Explain how, using bit shift, the unsigned binary number 00101100 can be divided by 4. [2 marks]

Answer 33

Shift right two places.

Question 34

00001100 is shifted two places to the left. Show the result. Identify what arithmetic operation this shift is equivalent to. [2 marks]

Answer 34

0011 0000 Multiplying by 4.

Question 35

An AND operation with the mask 10101010 is applied to the binary number 01010101. Show the result. [1 mark]

Answer 35

0000 0000

Question 36

An OR operation with the mask 10101010 is applied to the binary number 01010101. Show the result. [1 mark]

Answer 36

1111 1111

Question 37

Two floating point numbers are shown below. Calculate the answer of the second number subtracted from the first. You must show your working and ensure your answer is normalised. [5 marks] 01001100 0011 - 01001010 0010

Answer 37

01001110 0010