Digital Logic Design: Number systems and codes — Positional Number Systems and Base Conversion
How binary, octal and hexadecimal work, and how to convert whole numbers and fractions between bases.
Digital Logic Design · 24 questions
Try 3 questions
1. In a positional number system with base b, what is a digit's contribution to the total value?
- The digit times b raised to its position
- The digit times its position number
- The digit plus b times its position
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Answer: The digit times b raised to its position
Each position is worth a power of the base, so a digit d in position k (counting from 0 at the right) contributes d × b^k.
2. What decimal value does the binary number 1011 represent?
- 13
- 11
- 1011
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Answer: 11
1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11.
3. What is decimal 13 written in binary?
- 1011
- 1101
- 1110
Show the answer
Answer: 1101
13 = 8 + 4 + 1, so the 8, 4 and 1 positions are set: 1101.
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