Why does data have to be converted to binary to be processed by a computer?
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Why does data have to be converted to binary to be processed by a computer?
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).
Define binary data.
Binary data is data represented using the binary number system, consisting of only two digits: 1 and 0.
Why do computers use binary?
Computers are built using circuits and transistors. The circuits only need to check for two states:
On / off
True / False
North / south
1 / 0
Define binary number system.
The binary number system is a base-2 number system that represents numbers using only two digits: 0 and 1.
What is an example of binary representation in secondary storage devices?
An example of binary representation in secondary storage devices is magnetic hard drives, where North and South polarity represent 1 and 0.
Define transistor.
A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power.
What is the advantage of processing data in binary format for computers?
Processing data in binary format allows computers to perform complex calculations, store vast amounts of data efficiently, and operate at incredible speeds.
Define secondary storage.
Secondary storage refers to non-volatile storage devices that retain data even when the computer is turned off, such as hard drives and optical disks.
What is denary?
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.
Define binary number system.
The binary number system is a base-2 number system made up of two digits (1 and 0), where each digit has a weight factor of 2 raised to a power.
What is hexadecimal?
Hexadecimal is a base-16 number system made up of 16 digits, including 10 numbers (0-9) and 6 letters (A-F).
True or False?
In denary, the rightmost digit represents the 1s place.
True.
In denary, the rightmost digit represents the 1s place (10^0).
What is the weight factor of the second digit from the right in the binary system?
In the binary system, the second digit from the right has a weight factor of 2^1, which equals 2.
How many unique values can one hexadecimal digit represent?
One hexadecimal digit can represent 16 unique values (0-F).
What is a binary digit called?
A binary digit is called a bit.
True or False?
Hexadecimal uses the letters A-G to represent values 10-16.
False.
Hexadecimal uses the letters A-F to represent values 10-15.
What is the largest decimal number that can be represented by 8 bits in binary?
The largest decimal number that can be represented by 8 bits in binary is 255 (11111111 in binary).
How many bits does one hexadecimal digit represent?
One hexadecimal digit represents 4 bits (half a byte or one nibble).
What is denary?
Denary is a number system that is made up of 10 digits (0-9), also known as the Base-10 number system.
True or False?
Humans use the binary system for counting and performing math calculations.
False.
Humans use the denary system for counting, measuring, and performing math calculations.
Define binary.
Binary is a number system that is made up of two digits (1 and 0), also known as the Base-2 number system.
Why do computers use binary?
Computers use binary numbers to represent data because they are built using transistors that can only be in a state of on or off, which fits the binary number system of 1s and 0s.
True or False?
You may be asked to convert from/to binary up to and including 16 binary digits.
False.
You will only be asked to convert from/to binary up to and including 16 binary digits (2 bytes).
What is the denary range you will work with when converting to/from binary at GCSE level?
At GCSE level, you will work with a denary range of 0-65 536
(00000000 00000000 - 11111111 11111111 in binary).
Convert the following binary number to denary.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
128+0+32+0+8+4+0+0=172
Convert the following binary number to denary.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
0+64+32+16+0+0+0+1=113
Convert the following binary number to denary.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
128+0+0+16+0+0+0+0=144
Convert 76 to binary.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
Convert 150 to binary.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
Convert 94 to binary.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
What is hexadecimal?
Hexadecimal is a number system with 16 digits.
True or False?
Hexadecimal uses 16 digits.
True.
Hexadecimal uses 16 digits.
What is the relationship between hexadecimal and a binary nibble?
One hexadecimal digit represents four bits of binary data.
Define nibble.
A nibble is four bits of binary data or half a byte.
What is the non-mathematical method for converting denary to hexadecimal?
Convert denary to binary, split into nibbles, then convert each nibble to hexadecimal.
What is the mathematical method for converting denary to hexadecimal?
Divide denary by 16 and record the whole times (hex digit 1) and remainder (hex digit 2).
Example: Denary 160 to Hexadecimal = 160/16 = 10 (A) r 0 = A0
What is the non-mathematical method for converting hexadecimal to denary?
Convert each hexadecimal digit to 4-bit binary, join nibbles, then convert binary to denary.
What is the mathematical method for converting hexadecimal to denary?
Multiply the first digit by 16, then add the second digit.
Example: Hexadecimal B4 to denary = B (11) x 16 = 176 + 4 = 180
Convert denary 45 to hexadecimal.
Convert 45 to binary
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
Split in to 2 nibbles (4-bits)
0010 = 2
1101 = 13 (D)
Answer = 2D
Convert hexadecimal E7 to denary.
Convert each digit to 4-bit binary (nibble)
8 | 4 | 2 | 1 |
|---|---|---|---|
1 | 1 | 1 | 0 |
8 | 4 | 2 | 1 |
|---|---|---|---|
0 | 1 | 1 | 1 |
Combine to create an 8-bit value and convert to denary
11100111 = 231
Define nibble.
A nibble is a group of four bits.
What is the definition of binary?
Binary is a base-2 number system that uses only 0 and 1 to represent all values.
True or False?
Each digit in a hexadecimal number represents a binary nibble.
True.
Each digit in a hexadecimal number represents a binary nibble.
Define denary.
Denary is the base-10 number system, which uses digits from 0 to 9.
What does hexadecimal mean?
Hexadecimal is a base-16 number system that uses 16 digits: 0-9 and A-F.
State the method in terms of X for converting binary to hexadecimal.
Method:
Split X (binary number) into 2 x nibbles (4-bits)
Convert each nibble to its denary value
Represent each denary value as a hexadecimal digit.
Example: 11011001 = 1101 (13=D), 1001 (9) = D9
True or False?
To convert hexadecimal to binary, you split the digits apart and convert each to a binary nibble.
True.
To convert hexadecimal to binary, you split the digits apart and convert each to a binary nibble.
What is the definition of bit?
A bit is a basic unit of information in computing, representing either a 0 or 1.
Define byte.
A byte is a unit of digital information that consists of 8 bits.
Convert binary to hexadecimal.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 |
Split in to 2 nibbles (4-bits)
8 | 4 | 2 | 1 |
|---|---|---|---|
1 | 1 | 1 | 0 |
8 | 4 | 2 | 1 |
|---|---|---|---|
1 | 0 | 0 | 0 |
1110 = 14 (E)
1000 = 8
Answer = E8
Convert hexadecimal 4B to binary.
Convert each digit to a 4-bit binary value
8 | 4 | 2 | 1 |
|---|---|---|---|
0 | 1 | 0 | 0 |
8 | 4 | 2 | 1 |
|---|---|---|---|
1 | 0 | 1 | 1 |
Combine to create an 8-bit value
Answer = 01001011
Why is hexadecimal preferred when working with large values in Computer Science?
Hexadecimal is preferred because it takes fewer digits to represent a given value than binary, making it easier to read and less prone to errors when copying.
What does one hexadecimal digit correspond to in binary?
One hexadecimal digit corresponds to 4 bits (one nibble) and can represent 16 unique values (0-F).
Define MAC address.
A unique identifier for network interfaces, typically consisting of 12 hexadecimal digits.
True or False?
A typical MAC address consists of 12 hexadecimal digits, equivalent to 48 digits in binary.
True.
A typical MAC address consists of 12 hexadecimal digits, equivalent to 48 digits in binary.
True or False?
Hexadecimal can be used for colour codes.
True.
A six-digit hexadecimal number is used to represent colours in web design and digital graphics.
What is the format of a typical hexadecimal colour code?
A typical hexadecimal colour code consists of 6 hexadecimal digits, equivalent to 24 digits in binary. Each two-digit pair represents the colours red, green and blue
Define URL encoding.
The process of converting characters in a URL that are outside the standard set into hexadecimal codes.
True or False?
URLs can contain all types of characters without any encoding.
False.
URLs can only contain standard characters (a-z and A-Z), numbers (0-9), and some special symbols. Characters outside this set are converted into hexadecimal codes.
What are three common uses of hexadecimal in computing?
Three common uses of hexadecimal in computing are MAC addresses, colour codes, and URL encoding.
What is binary addition?
Binary addition is the process of adding together two binary integers (up to and including 8 bits).
True or False?
Binary addition starts from the rightmost digit and moves left.
True.
Binary addition starts from the rightmost digit and moves left.
What does "carrying over" mean in binary addition?
Carrying over occurs when the sum of a column is greater than 1, passing the excess to the next left column.
Define overflow error.
An overflow error is when the result of a binary addition exceeds the available bits.
What is 1 + 1 in binary addition?
1 + 1 = 10 (2 in denary)
True or False?
The sum of 1001 and 0100 in binary is 1101.
True.
The sum of 1001 and 0100 in binary is 1101.
What is the sum of 00011001 and 10000100 in binary?
The sum of 00011001 and 10000100 in binary is 10011101.
Define binary integer.
A binary integer is a number represented in the base 2 number system.
Perform the following binary addition
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Perform the following binary addition
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Perform the following binary addition
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | ||||
0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
Define binary shift.
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.
What does a left shift do?
A left shift multiplies a binary number by 2 (for every 1 place shift).
True or False?
A right shift divides a binary number by 2.
True.
A right shift divides a binary number by 2 (for every 1 place shift).
What is the definition of overflow error?
An overflow error occurs when a result is too large to be represented in the available storage space (needs more bits).
Define underflow error.
An underflow error occurs when a result is too small to be represented in the available storage space.
State the equation in terms of X for a left shift of 2 places.
X << 2 (X shifted left by 2 places) = X * 4
True or False?
A left shift of 3 places multiplies the binary number by 8.
True.
A left shift of 3 places multiplies the binary number by 8.
In binary shifts, what is the definition of precision?
In binary shifts, precision refers to the number of digits used to represent a value.
Define bit.
A bit is a basic unit of information in computing, representing either a 0 or 1.
What does binary multiplication mean?
Binary multiplication refers to the process of multiplying binary numbers using shifts and additions.
Define Two's complement.
A method of using signed binary values to represent negative numbers, where the leftmost bit is designated as the most significant bit (MSB).
How is a negative number represented in two's complement?
In two's complement, a negative number is represented by setting the most significant bit (MSB) to 1.
Define MSB.
The Most Significant Bit, which in two's complement represents the sign of the number (0 for positive, 1 for negative).
In 8-bit two's complement, what is the value of the leftmost column?
In 8-bit two's complement, the value of the leftmost column is -128.
What is the two's complement representation of -1 in 8 bits?
The two's complement representation of -1 in 8 bits is 11111111.
True or False?
In two's complement, positive numbers are represented the same way as in unsigned binary.
True.
In two's complement, positive numbers are represented the same way as in unsigned binary.
What is a quick method to perform a two's complement conversion?
A method to convert a positive number to its negative two's complement representation by inverting all bits after the rightmost 1.
What is the first step in the quick two's complement conversion?
The first step in the quick two's complement conversion is to write out the positive version of the number in binary.
True or False?
In the quick two's complement conversion, you invert all bits including and after the first 1 from the right.
False.
In the quick two's complement conversion, you copy bits up to and including the first 1 from the right, then invert the remaining bits.
What is the two's complement representation of -76 in 8 bits?
The two's complement representation of -76 in 8 bits is 10110100.