Convert the following Binary numbers into Decimal numbers.a. 10101
The correct answer and explanation is:
✅ Correct Answer:
Binary 10101 = Decimal 21
🧠 Step-by-Step Explanation:
Binary numbers are based on the base-2 numeral system, which uses only two digits: 0 and 1. Each digit (called a bit) represents an increasing power of 2, starting from the rightmost digit (least significant bit).
To convert binary 10101 to decimal:
Write the binary number with positional powers of 2:
Binary: 1 0 1 0 1
Position: 4 3 2 1 0 → (these are the exponents for base 2)
Now calculate the value of each bit:
- 1×24=161 × 2^4 = 16
- 0×23=00 × 2^3 = 0
- 1×22=41 × 2^2 = 4
- 0×21=00 × 2^1 = 0
- 1×20=11 × 2^0 = 1
Add them all up:
16+0+4+0+1=2116 + 0 + 4 + 0 + 1 = \boxed{21}
📘 Why This Works:
The decimal system (base-10) is what we use in everyday life. The binary system (base-2) is used by computers and digital systems because it’s simple and efficient for representing on/off states with 1s and 0s.
Each digit in a binary number represents an increasing power of 2 from right to left. The digit tells us whether that power of 2 should be included (1) or ignored (0).
So in 10101, we’re including:
- 24=162^4 = 16,
- 22=42^2 = 4,
- 20=12^0 = 1,
Which totals to 21.
✅ Final Answer:
Binary 10101 = Decimal 21