Convert the decimal number 220 into binary, Convert the hexadecimal number AD into binary - AQA - GCSE Computer Science - Question 1 - 2021 - Paper 1

To convert the hexadecimal number AD into binary, we convert each hex digit to its 4-bit binary equivalent:

• A in hex is 1010 in binary
• D in hex is 1101 in binary

Therefore, AD in binary is:

$AD_{16} = 1010 1101_{2}$

To convert the hexadecimal number 1A into decimal, we can use the positional value method:

• The positional values for 1A are:
  • 1 is in the 16's place (1 × 16^1)
  • A (10 in decimal) is in the 1's place (10 × 16^0)

Thus, we calculate:

$1 × 16^{1} + 10 × 16^{0} = 16 + 10 = 26$

Hence, the decimal value of 1A is 26.

The largest hexadecimal number that can be represented in binary using 8 bits is represented by 8 bits all set to 1:

This value in binary would be:

$11111111_{2}$

In hexadecimal, this is:

$FF_{16}$.