The decimal number 28 would be written in binary as

a) 11100

b) 00111

c) 10110

d) 01011

The octal number 62 would be written in decimal as a) A12 b) F35 c) 50 d) 98 The hexadecimal number C4 would be written in decimal as a) 21 b) 48 c) 182 d) 196

The correct answer and explanation is :

Let’s solve each of the three number conversion questions and then provide a clear explanation.

1. The decimal number 28 in binary is:

To convert 28 from decimal to binary:

28 ÷ 2 = 14, remainder 0
14 ÷ 2 = 7, remainder 0
7 ÷ 2 = 3, remainder 1
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1

Reading remainders from bottom to top: 11100

✅ Correct Answer: a) 11100

2. The octal number 62 in decimal is:

Octal is base-8. To convert 62 (octal) to decimal:

$6 \times 8^1 + 2 \times 8^0 = 48 + 2 = 50$

✅ Correct Answer: c) 50

3. The hexadecimal number C4 in decimal is:

Hexadecimal is base-16. In hex, C = 12, so:

$12 \times 16^1 + 4 \times 16^0 = 192 + 4 = 196$

✅ Correct Answer: d) 196

🔍 Explanation (300 words)

Understanding how number systems work is essential in computing and digital electronics. Let’s break it down:

Binary (Base-2)

Binary uses only two digits: 0 and 1. Each digit represents a power of 2. To convert a decimal number like 28 to binary, divide it repeatedly by 2 and record the remainders. Reading these remainders in reverse gives us the binary number. For 28, the binary form is 11100, which means:

$1×2^4 + 1×2^3 + 1×2^2 + 0×2^1 + 0×2^0 = 28$

Octal (Base-8)

The octal system uses digits from 0 to 7. To convert an octal number like 62 to decimal, expand it using powers of 8:

$6×8^1 + 2×8^0 = 48 + 2 = 50$

Octal is especially useful in computing because it shortens binary representations (3 binary digits per octal digit).

Hexadecimal (Base-16)

Hex uses digits 0–9 and letters A–F (where A=10 to F=15). It’s a compact form to represent binary data (4 binary digits per hex digit). For C4, we convert:

C = 12, so $12×16^1 + 4×16^0 = 192 + 4 = 196$

This method is widely used in memory addressing and color codes in web development.

Conclusion

Each system serves a specific purpose in computing. Binary is foundational, octal and hexadecimal provide compact alternatives, and understanding conversions between them is vital for programming, data encoding, and hardware design.