Font size
WorksheetsY11 Hex & Binary Homework
Total questions: 56
Worksheet time: 2hrs 13mins
In a computer, all data is stored in binary form. A binary digit has two possible states, 1 and 0.
A binary digit is known as a bit. A bit is the smallest unit of data a computer can use. The binary unit system is used to describe bigger numbers too.
Eight bits are known as a byte.
Analogue data is a real-life signal that can vary greatly in value. Examples include:
sound waves
pressure
temperature
Digital data is binary data which represents analogue data. Computers work with digital data. Analogue data must be converted to digital before a computer can use it. A device known as an analogue-to-digital convertor (ADC) is used to generate digital data from analogue signals. In the same way, a digital signal can be converted back to an analogue signal using a digital-to-analogue convertor (DAC).
What is a byte?
A unit of measurement for data storage
A type of computer programming language
A type of computer hardware
A unit of measurement for time
In what form is all data stored in a computer?
Decimal form
Binary form
Hexadecimal form
Octal form
What is the smallest unit of data a computer can use?
Byte
Nibble
Bit
Word
Humans tend to use the denary number system. However, computers work in binary. Denary numbers must be converted into their binary equivalent before a computer can use them.
The denary system has ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9). Each denary place value is calculated by multiplying the previous place value by ten. For example:
10,0001,000100101
So, the value of the number 124 in denary place values is actually:
Place value10,0001,000100101Value00124
This gives (1 × 100) + (2 × 10) + (1 × 4) = 124
Binary to denary
Binary has just two units, 0 and 1. The value of each binary place value is calculated by multiplying the previous place value by two. The first eight binary place values are:
1286432168421
In binary, each place value can only be represented by 1 or a 0.
To convert binary to denary, simply take each place value that has a 1, and add them together.
Example - binary number 1111100
128643216842101111100
Result: (0 × 128) + (1 × 64) + (1 × 32) + (1 × 16) + (1 × 8) + (1 × 4) + (0 × 2) + (0 × 1) = 124
How is each place value calculated in binary?
By adding the previous place value to two
By multiplying the previous place value by two
By dividing the previous place value by two
By subtracting the previous place value from two
What must be done before a computer can use denary numbers?
Convert them to binary
Convert them to hexadecimal
Convert them to octal
Convert them to Roman numerals
What is the denary system?
A system with eight digits
A system with twelve digits
A system with ten digits
A system with six digits
What is the process to convert binary to denary?
Take each place value that has a 1 and add them together
Take each place value that has a 0 and add them together
Multiply each place value by 2 and add them together
Divide each place value by 2 and add them together
What number system do computers work in?
Binary
Denary
Octal
Hexadecimal
What does "bit" mean?
Binary digit
Binary number
Decimal digit
Binomial dropit
A
10
B
11
C
12
D
13
E
14
Reorder the following in ascending order
0010
0011
0100
1010
1100
Which of the following is a hexadecimal number?
101
10100111
52086
12547896412
8888B88888
Convert 145 to binary
(a)
Convert 245 to binary
(a)
Convert 178 to binary
(a)
Convert 10110 to denary
(a)
Convert 1011110 to denary
(a)
Convert 11001101 to denary
(a)
Convert A1 to binary
(a)
Convert FF9 to binary
(a)
Convert 78A
(a)
Convert 1010111 to hexadecimal
(a)
Convert 11001100 to hexadecimal
(a)
Convert 11101111 to hexadecimal
(a)
Reorder the following in descending order
FA16
20110
110000112
B416
100000102
Convert the hexadecimal number 3A to binary.
00101011
00111010
11001100
10101010
Convert the binary number 10101011 to hexadecimal.
AB
EF
CD
BA
Convert the hexadecimal number 7F to binary.
10111111
11111111
00111111
01111111
Convert the binary number 11001101 to hexadecimal.
1CD
CD
DD
12C
Convert the hexadecimal number A5 to binary.
10100101
01010101
11110000
11001100
Convert the binary number 11110000 to hexadecimal.
EE
DD
F0
FF
Convert the hexadecimal number 2B to binary.
11010101
10010101
01010101
00101011
Convert the binary number 10011010 to hexadecimal.
8B
1A
9A
C3
Convert the hexadecimal number F8 to binary.
11001100
11111000
10101010
10011000
In computer science, different number bases are used:
denary is base 10, which has ten units (0-9)
binary is base 2 , which has two units (0-1)
Hexadecimal, also known as hex, is the third commonly used number system. It has 16 units (0-9) and the letters A, B, C, D, E and F.
Hex is useful because large numbers can be represented using fewer digits. For example, colour values and MAC addresses are often represented in hex.
Additionally, hex is easier to understand than binary. Programmers often use hex to represent binary values as they are simpler to write and check than when using binary.
Hexadecimal to denary
Whereas denary place values are powers of 10, and binary place values are powers of 2, hex place values are powers of 16.
65,5364,096256161
Each place value can be represented by the units 0 through to F.
To convert hex to denary, simply take each place value that has a unit in it, and add them together.
Example - hex number 7C
65,5364,0962561617C
Result: (7 × 16) + (C × 1) = (7 × 16) + (12 × 1) = (112) + (12) = 124
What are the place values in hexadecimal?
Powers of 2
Powers of 8
Powers of 10
Powers of 16
Which number base is easier to understand than binary?
Octal
Hexadecimal
Decimal
Binary
What is one advantage of using hexadecimal?
It is the easiest number base to understand
It is useful for representing large numbers with fewer digits
It is the most commonly used number base in computer science
It is only used for representing small numbers
What is the process to convert hex to denary?
Multiply the place values with units
Subtract the place values with units
Divide the place values with units
Add up the place values with units
What is the number of units in the hexadecimal number system?
8
10
12
16
Convert the binary number 11111111 to hexadecimal.
AA
DD
CC
FF
Convert the hexadecimal value 11 to 8-bit binary
(a)
Convert the hexadecimal value 12 to 8-bit binary
(a)
Convert the hexadecimal value 20 to 8-bit binary
(a)
Convert the hexadecimal value 26 to 8-bit binary
(a)
Convert the hexadecimal value 60 to 8-bit binary
(a)
Convert the hexadecimal value 60 to 8-bit binary
(a)
Convert the hexadecimal value 6A to 8-bit binary
(a)
Convert the hexadecimal value 3D to 8-bit binary
(a)
Convert the hexadecimal value 8F to 8-bit binary
(a)
Convert the hexadecimal value FF to 8-bit binary
(a)
Convert the hexadecimal value 0F to 8-bit binary
(a)
Convert the 8-bit binary number 11110010 to hexadecimal
(a)
Convert the 8-bit binary number 11111010 to hexadecimal
(a)
Convert the 8-bit binary number 10101010 to hexadecimal
(a)
Convert the 8-bit binary number 10101011 to hexadecimal
(a)
Convert the 8-bit binary number 11000100 to hexadecimal
(a)
Convert the 8-bit binary number 11010101 to hexadecimal
(a)
Convert the 8-bit binary number 10101001 to hexadecimal
(a)
Convert the 8-bit binary number 01011011 to hexadecimal
(a)
Convert the 8-bit binary number 11001100 to hexadecimal
(a)
Calculate the binary addition:
01100000
01101001
Use binary addition rules
11001001
11101001
11001011
1010101111
Calculate the binary addition:
01101111
01101111
Use binary addition rules
11011110
11011111
11111110
11111110
Calculate the binary addition:
00111011
00110011
Use binary addition rules
01101111
01111110
01101110
11111110
Calculate the binary addition:
01100000
01101001
Use binary addition rules
11001001
11101001
11001011
1010101111
Calculate the binary addition:
01101111
01101111
Use binary addition rules
11011110
11011111
11111110
11111110
Calculate the binary addition:
00111011
00110011
Use binary addition rules
01101111
01111110
01101110
11111110
