Question

Give a procedure for converting from the hexadecimal expansion of an integer to its octal expansion using binary notation as an intermediate step.

Short answer

Algorithm: 1) Convert hexadecimal to binary by writing the 4 bit binary equivalent of each hex digit

2) group the bits from right to left in groups of 3. For the leftmost ungrouped bits, append 0s to make the entire number contain 3k bits.

3) write down the octal equivalent of each group

Step-by-step solution

Step 1:

Algorithm: 1) Convert hexadecimal to binary by writing the 4 bit binary equivalent of each hex digit

2) group the bits from right to left in groups of 3. For the leftmost ungrouped bits, append 0s to make the entire number contain 3k bits.

3) write down the octal equivalent of each group

Example: Hex: f binary equivalent is: 1111 group into 3 and append 0s: (001) (111) octal: 17