Decimal to Hexadecimal — Division and Remainder Convert the decimal number 74 to its hexadecimal form, showing the division by 16 process or an equivalent mental shortcut.

Introduction / Context:
Decimal to hexadecimal conversion is frequent when interpreting addresses, constants, or color codes. The process uses repeated division by 16 and collecting remainders, or a quick decomposition into 16s and units if the number is small.

Given Data / Assumptions:

• Decimal input: 74.
• Hex digit values: 10→A, 11→B, ... 15→F.
• No sign and no fractional part.

Concept / Approach:
Compute the quotient and remainder when dividing by 16. The quotient gives the high hex digit and the remainder gives the low hex digit. Alternatively, write 74 = 416 + 10 and map 10 to A directly.

Step-by-Step Solution:
1) Perform division: 74 / 16 = 4 remainder 10.2) Map remainder 10 to hex A.3) High digit is 4 and low digit is A.4) Combine to get 4A base 16, written as 4A16.

Verification / Alternative check:
Convert back: 4A16 = 416 + A = 64 + 10 = 74 decimal. The round trip confirms the value.

Why Other Options Are Wrong:

• A416 and B416: These represent 164 and 180 decimal respectively, not 74.
• 4B16: Equals 4*16 + 11 = 75, not 74.

Common Pitfalls:
Forgetting that A denotes 10, misreading the remainder, or reversing the order of quotient and remainder when forming the hex digits.

Final Answer:
4A16