ITPEC FE Morning October 2021 Question 1

3665 — go through binary: each hex digit is 4 bits and each octal digit is 3 bits.

• •Hex to binary: 7 = 0111, B = 1011, 5 = 0101, giving 011110110101
• •Regroup in threes from the right: 011 110 110 101
• •Read each group as an octal digit: 3, 6, 6, 5

Check in decimal: 7 × 256 + 11 × 16 + 5 = 1973 and 3 × 512 + 6 × 64 + 6 × 8 + 5 = 1973.

Answer (b)

Why not others:

• •(a) 735 — only three octal digits, so at most 511 in decimal, far below 1973; 12 bits need four octal digits
• •(c) 7551 and (d) 7561 — a leading 7 needs the top three bits to be 111, but 7B5 starts with 011; these values (3945 and 3953 in decimal) are about twice 1973

Key rule: To convert between hex and octal, write out the bits and regroup them from the right: 4 bits per hex digit, 3 bits per octal digit.

Basic Theory · AI-written, may contain errors