The disaster-response team labels encrypted radio messages with a hexadecimal checksum. One message has checksum 6F3. Before the team uses it in a denary ve...
Question 1 Report
The disaster-response team labels encrypted radio messages with a hexadecimal checksum. One message has checksum 6F3. Before the team uses it in a denary verification algorithm, the computer must convert the value and identify the largest checksum that can use three hexadecimal digits.
(a) Give the denary value of hexadecimal 6F3. [3]
(b) Give the 12-bit binary value of hexadecimal 6F3. [3]
(c) State the greatest denary value of a three-digit hexadecimal checksum. [2]
(d) Explain why hexadecimal checksums are often used in technical reports instead of binary strings. [1]
Answer Details
(a) Hexadecimal F represents \(15\):
\[6F3_{16}=(6\times256)+(15\times16)+3=1536+240+3=1779\]
The denary value is 1779. [3]
(b) Convert each digit to four bits:
\[6=0110,\quad F=1111,\quad 3=0011\]
The 12-bit value is 011011110011. [3]
(c) The greatest three-digit hexadecimal checksum is FFF, equal to 4095 in denary. [2]
(d) Hexadecimal checksums are more compact than binary strings and easier for people to read and copy accurately. [1]
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