Converting Between Denary & Hexadecimal (OCR GCSE Computer Science): Revision Notes

Question**:** Convert 172 to hex

Step 1: Divide the denary number by 16

• When converting denary to hexadecimal, the first step is to divide the denary number by 16.
• In this case, we are converting 172 to hex.
• So, we divide 172 by 16: 172 ÷ 16 = 10 remainder 12.

Step 2: Interpret the quotient (whole number result)

• The quotient from the division represents the leftmost hex digit.
• Here, the quotient is 10.
• In hexadecimal, the number 10 is written as the letter A.
• So, the leftmost hex digit is A.

Step 3: Interpret the remainder

• The remainder of the division represents the rightmost hex digit.
• The remainder is 12.
• In hexadecimal, the number 12 is written as the letter C.
• So, the rightmost hex digit is C.

Final Answer: Combine the two hex digits

• Now that we have both hex digits (A and C), we combine them.
• Therefore, 172 in hex is written as AC.

Question**:** Convert 172 to hex

Step 1: Convert the denary number to an 8-bit binary number

• First, we convert the denary number (172) into its binary form.
• In binary, 172 is written as 10101100.
• We use 8 bits because it's a standard format for representing numbers in binary (ensuring two hexadecimal digits).

Step 2: Split the binary number into two 4-bit nibbles

• Next, we split the 8-bit binary number into two groups of 4 bits, called "nibbles."
• The first 4 bits are 1010 and the second 4 bits are 1100.

Step 3: Convert each nibble to its hex equivalent

• Now, we convert each nibble (group of 4 bits) to its hexadecimal equivalent:
• 1010 in binary is A in hexadecimal.
• 1100 in binary is C in hexadecimal.

Final Answer: Combine the two hex digits

• Finally, we combine the two hex digits, A and C.
• Therefore, 172 in hex is written as AC.

Question**:** Convert 3F to denary

Step 1: Multiply the left hex digit by 16

• The leftmost digit in a hexadecimal number represents the "16s place" because hex is base 16.
• In this example, the left hex digit is 3.
• Multiply 3 by 16 3 × 16 = 48.
• This gives us the value contributed by the left digit.

Step 2: Multiply the right hex digit by 1

• The rightmost digit represents the "1s place" in hexadecimal.
• In this example, the right hex digit is F, which is 15 in denary.
• Multiply 15 by 1 15 × 1 = 15.
• This gives us the value contributed by the right digit.

Step 3: Add the two values together

• Finally, add the two values from the previous steps: 48 + 15 = 63.

Final Answer: Denary equivalent

• Therefore, the hexadecimal number 3F is equal to 63 in denary.

Key Points to Remember

• Hexadecimal is a base-16 system using digits 0-9 and letters A-F (where A=10, B=11, ... F=15).
• To convert denary to hexadecimal, divide by 16 and use the quotient and remainder as hex digits.
• Alternatively, convert denary to binary, split the binary into 4-bit nibbles, and convert each to hex.
• To convert hexadecimal to denary, multiply the left digit by 16 and the right digit by 1, then add the results.