Questions: Binary Number System

Question 1

What is the decimal value of the binary number 1101?

• A. 10
• B. 11
• C. 13
• D. 14

Answer: (C)

Each bit position is a power of 2: 1×8 + 1×4 + 0×2 + 1×1 = 8 + 4 + 0 + 1 = 13. A common error is reading the bits as if they were decimal digits (1101 = 1,101 in decimal), which confuses binary representation with its decimal meaning.

Question 2

Leading zeros change the value of a binary number (e.g., 0101 has a different value than 101).

• T. True
• F. False

Answer: False

Just as 007 equals 7 in decimal, 0101 equals 101 in binary — both represent the value 5. Leading zeros are only written for practical reasons like aligning numbers to a fixed bit-width (e.g., writing 8-bit values always as 8 digits).

Question 3

Why do computers use binary rather than decimal to represent all data?

Model answer: Electronic circuits have two stable physical states — high voltage and low voltage (or on and off) — which map directly to 1 and 0. Reliably distinguishing ten voltage levels for decimal would be far more error-prone and expensive to engineer.

Binary is not just a convention but a physical match to how transistors work. A transistor is either conducting or not — two states. Encoding more states per circuit element would require finer voltage discrimination, making hardware more complex, slower, and less reliable.