Binary Representation

1. What is Binary Representation?
Binary is a number system that uses only two digits: 0 and 1. It is the foundational number system in computing.

2. How do you convert from Binary to Decimal?
To convert binary to decimal, multiply each bit by 2 raised to the power of its position (starting from 0 on the far right) and then sum the results.

3. How do you convert from Decimal to Binary?
To convert decimal to binary, repeatedly divide the decimal number by 2, recording the remainders. Read the remainders from bottom to top to get the binary equivalent.

4. How do you convert from Binary to Hexadecimal?
Group the binary digits in sets of four (starting from the right), then convert each group to its hexadecimal equivalent.

5. How do you convert from Hexadecimal to Binary?
Convert each hexadecimal digit into its 4-bit binary equivalent.

6. What is Two's Complement?
Two's complement is a method for representing negative numbers in binary. It involves inverting all bits and adding 1 to the result.

7. How do you find the two’s complement of a binary number?

  1. Invert all the bits (change 0s to 1s and 1s to 0s).

  2. Add 1 to the result.

8. What is the range of values for an 8-bit two's complement number?
The range is from -128 to +127.

9. How do you convert a positive decimal number to binary?
For positive decimal numbers, use repeated division by 2, noting the remainders until you reach zero. The binary number is the list of remainders read from bottom to top.

10. How do you convert a negative decimal number to binary using two's complement?

  1. Convert the positive version of the decimal number to binary.

  2. Apply two’s complement (invert the bits and add 1).