number systems

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).

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

Computers are built using circuits and transistors. The circuits only need to check for two states:

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

An example of binary representation in secondary storage devices is magnetic hard drives, where North and South polarity represent 1 and 0.

A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power.

Processing data in binary format allows computers to perform complex calculations, store vast amounts of data efficiently, and operate at incredible speeds.

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.

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.

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.

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

True. In denary, the rightmost digit represents the 1s place (10^0).

In the binary system, the second digit from the right has a weight factor of 2^1, which equals 2.

One hexadecimal digit can represent 16 unique values (0-F).

A binary digit is called a bit.

False. ** Hexadecimal uses the letters A-F to represent values 10-15**.

The largest decimal number that can be represented by 8 bits in binary is 255 (11111111 in binary).

One hexadecimal digit represents 4 bits (half a byte or one nibble).

Denary is a number system that is made up of 10 digits (0-9), also known as the Base-10 number system.

False. Humans use the denary system for counting, measuring, and performing math calculations.

Binary is a number system that is made up of two digits (1 and 0), also known as the Base-2 number system.

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.

False. You will only be asked to convert from/to binary up to and including 16 binary digits (2 bytes).

At GCSE level, you will work with a denary range of 0-65 536(00000000 00000000 - 11111111 11111111 in binary).

128+0+32+0+8+4+0+0=172

0+64+32+16+0+0+0+1=113

128+0+0+16+0+0+0+0=144

Hexadecimal is a number system with 16 digits.

True. Hexadecimal uses 16 digits.

One hexadecimal digit represents four bits of binary data.

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

Convert denary to binary, split into nibbles, then convert each nibble 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

Convert each hexadecimal digit to 4-bit binary, join nibbles, then convert binary 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 45 to binary Split in to 2 nibbles (4-bits) 0010 = 21101 = 13 (D)Answer = 2D

Convert each digit to 4-bit binary (nibble) Combine to create an 8-bit value and convert to denary11100111 = 231

A nibble is a group of four bits.

Binary is a base-2 number system that uses only 0 and 1 to represent all values.

True. Each digit in a hexadecimal number represents a binary nibble.

Denary is the base-10 number system, which uses digits from 0 to 9.

Hexadecimal is a base-16 number system that uses 16 digits: 0-9 and A-F.

Method: Example: 11011001 = 1101 (13=D), 1001 (9) = D9

True. To convert hexadecimal to binary, you split the digits apart and convert each to a binary nibble.

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

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

Split in to 2 nibbles (4-bits) 1110 = 14 (E)1000 = 8Answer = E8

Convert each digit to a 4-bit binary value Combine to create an 8-bit valueAnswer = 01001011

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.

One hexadecimal digit corresponds to 4 bits (one nibble) and can represent 16 unique values (0-F).

A unique identifier for network interfaces, typically consisting of 12 hexadecimal digits.

True. A typical MAC address consists of 12 hexadecimal digits, equivalent to 48 digits in binary.

True. A six-digit hexadecimal number is used to represent colours in web design and digital graphics.

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

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

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.

Three common uses of hexadecimal in computing are MAC addresses, colour codes, and URL encoding.

Binary addition is the process of adding together two binary integers (up to and including 8 bits).

True. Binary addition starts from the rightmost digit and moves left.

Carrying over occurs when the sum of a column is greater than 1, passing the excess to the next left column.

An overflow error is when the result of a binary addition exceeds the available bits.

1 + 1 = 10 (2 in denary)

True. The sum of 1001 and 0100 in binary is 1101.

The sum of 00011001 and 10000100 in binary is 10011101.

A binary integer is a number represented in the base 2 number system.

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.

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

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

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

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

X << 2 (X shifted left by 2 places) = X * 4

True. A left shift of 3 places multiplies the binary number by 8.

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

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

Binary multiplication refers to the process of multiplying binary numbers using shifts and additions.

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

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

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, the value of the leftmost column is -128.

The two's complement representation of -1 in 8 bits is 11111111.

True. In two's complement, positive numbers are represented the same way as in unsigned binary.

A method to convert a positive number to its negative two's complement representation by inverting all bits after the rightmost 1.

The first step in the quick two's complement conversion is to write out the positive version of the number in binary.

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.

The two's complement representation of -76 in 8 bits is 10110100.