Number Systems And Binary Flashcards
What are the two binary digits?
0 and 1
What is the largest binary number that can be stored in 8 bits?
255 in decimal (binary: 11111111).
What is the binary representation for the decimal number 134?
10000110 (128 + 4 + 2).
Convert the binary number 011 to decimal.
3
Convert the binary number 0110 to decimal.
6
Convert the binary number 1001 to decimal.
9
Convert the binary number 1010 to decimal.
10
Convert the decimal number 5 to binary.
0101
Convert the decimal number 7 to binary.
0111
Convert the decimal number 26 to binary.
0011010
What do binary fractions use after the binary point?
Positions (e.g., 0.5, 0.25).
What is the binary representation for 136.75?
10001000.11 (128 + 8 + 0.5 + 0.25).
What is a mixed number in binary?
Uses fixed bits for integers and fractions.
What does 110011.01 equal in decimal?
51.25
How to represent -5 in binary (using 8 bits)?
Convert 5 to binary: 00000101, flip the bits: 11111010, add 1: 11111011.
How to represent -66 in binary (using 8 bits)?
Start with positive 66: 01000010, flip the bits: 10111101, add 1: 10111110.
What are the addition rules in binary?
0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 0 (carry 1).
What is an example of binary addition?
00011 + 00001 = 00100
How to perform binary subtraction?
Convert second number to two’s complement and add.
What is an example of binary subtraction?
12 - 9: 9: 00001001, Two’s complement: 11110111, Add to 12: 00001100 + 11110111 = 00000011 (3)
What are the steps for binary multiplication?
Write binary numbers in a table, perform long multiplication (shift and add method).
What is an example of binary multiplication?
8 (1000) × 3 (11) = 11000 (24).
What is the binary multiplication of 8 × 2?
1000 × 10 = 10000 (16).
What is the binary multiplication of 12 × 10?
1100 × 1010 = 1111000 (120).
What is the repeated division-by-2 method?
A method to convert a decimal number to binary by dividing the number by 2 repeatedly and recording the remainders. The least significant bit (LSB) is at the top, and the most significant bit (MSB) is at the bottom.
Convert the decimal number 294 to binary.
Using the division-by-2 method, 294 in binary is 100100110.
Convert the decimal number 89 to binary.
Using the division-by-2 method, 89 in binary is 1011001.
What is hexadecimal?
Hexadecimal is a base-16 numbering system using digits 0-9 and letters A-F. It is often used in computing for its compact representation of binary values.
How do you convert binary to hexadecimal?
Group the binary number into 4-bit sections from right to left and convert each group into its hexadecimal equivalent.
Convert the binary number 10010010 to hexadecimal.
Grouping into 4-bit sections: **1001 0010 The hexadecimal equivalent is **92
What are the benefits of hexadecimal?
- Easier to read and understand than long binary strings.
- Compact representation of binary data.
- Reduces the chance of errors when typing or interpreting.
Convert the hexadecimal number 3CF to binary.
Convert each hexadecimal digit: 3 = 0011, C = 1100, F = 1111. The binary equivalent is 001111001111.
What are the components of floating-point numbers?
- Significant: The main number digits.
- Exponent: Determines the position of the decimal or binary point relative to the significant digits.
Why are floating-point numbers needed?
They allow for the representation of very large or very small numbers in a compact format, suitable for scientific calculations and data storage.
What is absolute error?
The difference between the estimated value and the actual value. For example, if the actual value is 20 and the estimated value is 18, the absolute error is 2.
What is relative error?
The ratio of the absolute error to the actual value. For example, if the actual value is 20 and the absolute error is 2, the relative error is 2/20 = 0.1 or 10%.
What are the limitations of floating-point numbers?
- Limited precision, leading to rounding errors.
- Cannot exactly represent some numbers.
- Susceptible to overflow and underflow in calculations.
What are natural numbers and integers?
- Natural Numbers (N): Whole numbers starting from 0 (e.g., 0, 1, 2…).
- Integers (Z): Whole numbers including negatives (e.g., -3, -2, -1, 0, 1, 2…).
What is the difference between rational and irrational numbers?
- Rational Numbers (Q): Numbers that can be expressed as a fraction (e.g., 7/1).
- Irrational Numbers: Numbers that cannot be expressed as a fraction (e.g., √2).
What is a real number?
Rational and irrational numbers as a group
What is a rounding error?
Decimal converted to floating point but can’t be represented exactly in available number of bits.
