1.1 Number systems Flashcards
(25 cards)
Why do computers use binary to represent all forms of data?
Computers use binary because they can only recognize two states, typically represented as 0 (off) and 1 (on). This system simplifies data processing and storage using logic gates and registers.
What is the denary number system?
The denary (or decimal) system is a base 10 number system that uses values from 0 to 9. It’s the most commonly used system in everyday life.
What is the binary number system?
The binary system is a base 2 system, meaning it only uses two values: 0 and 1. It is used by computers for data processing.
What is the hexadecimal number system?
Hexadecimal is a base 16 number system that uses values from 0 to 9 and A to F, where A represents 10, B represents 11, and so on up to F, which represents 15.
How do you convert binary to hexadecimal?
Divide the binary value into groups of four bits, starting from the right. If necessary, add leading zeros. Then, convert each group to its hexadecimal equivalent.
How do you convert hexadecimal to binary?
Convert each hexadecimal digit to a 4-bit binary number and then combine them all together.
How do you convert denary to binary?
Divide the denary value by 2 successively, recording the remainder at each step. The binary number is the sequence of remainders read from bottom to top.
How do you convert binary to denary?
Multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right), and then add the results together.
What happens when you add binary numbers?
Binary addition follows these rules:
0 + 0 = 0
1 + 0 = 1 (and vice versa)
1 + 1 = 0 with a carry of 1
1 + 1 + 1 = 1 with a carry of 1
What is binary overflow?
Overflow occurs when the result of a binary operation exceeds the maximum value that can be represented by the given number of bits, such as exceeding 8 bits in an 8-bit system.
What is two’s complement?
Two’s complement is a method for representing negative binary numbers. The most significant bit (MSB) represents the sign, and negative values are represented by inverting all the bits and adding 1 to the result.
How do you convert a positive binary number to two’s complement?
To convert a positive binary number to two’s complement, just ensure that the MSB is 0. Negative numbers require inverting the bits and adding 1.
How do you convert a negative number to two’s complement?
To convert a negative number to two’s complement, find its positive binary equivalent, invert all the bits, and then add 1.
How do you convert a two’s complement binary value to denary?
If the MSB is 1, convert the binary value to its positive equivalent by inverting the bits, adding 1, and then applying the negative sign. If the MSB is 0, convert normally.
What is a logical binary shift?
A logical shift moves bits to the left or right. In a left shift, zeros are added to the right, and in a right shift, zeros are added to the left.
What happens in a logical left shift of a binary number?
In a logical left shift, the bits of the binary number move to the left, and a 0 is added to the rightmost position. This operation effectively multiplies the number by 2.
What happens in a logical right shift of a binary number?
In a logical right shift, the bits of the binary number move to the right, and a 0 is added to the leftmost position. This operation effectively divides the number by 2.
Why is hexadecimal used in computing?
Hexadecimal is used because it is a more compact and human-readable representation of binary values. Each hexadecimal digit represents four binary digits (bits), making it easier to work with.
How do you convert hexadecimal to denary?
Convert each hexadecimal digit to its binary equivalent, then convert the binary number to denary by multiplying each bit by the corresponding power of 2.
How do you convert denary to hexadecimal?
Divide the denary number by 16, record the remainders, and read the remainders from bottom to top. Each remainder corresponds to a hexadecimal digit.
What is the result of adding 1101110 and 1101110 in binary?
The binary addition gives the result of 1101110 + 1101110 = 11011100, with an overflow since it exceeds 7 bits.
What happens if two binary numbers exceed the 8-bit limit?
An overflow error occurs. For example, adding two 8-bit numbers, 11111111 and 00000001, results in 100000000, which exceeds the 8-bit limit.
Convert the hexadecimal value 2AF to binary.
2AF in hexadecimal converts to 0010 1010 1111 in binary.
Add the binary numbers 11001010 and 10110101.
The result is 101111111, which exceeds 8 bits and causes an overflow.
