A number's radix is its base: the number of different digits it uses. Each position has a weight equal to a power of that base. The rightmost integer position has weight one; positions to its left become progressively larger.
Worked example
In decimal, 243 means 2 × 100 + 4 × 10 + 3 × 1. In binary, 1011 means 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 11 in decimal. The written digits look similar, but their weights differ.
What to watch for
Always label the base when a number could be ambiguous. The string 10 represents ten in decimal and two in binary.
Try it yourself
What decimal value does binary 110 represent?
Answer: Its weights are 4, 2 and 1. Therefore 1 × 4 + 1 × 2 + 0 × 1 = 6.
How to study this topic
Write the base and bit width beside every value. Expand place weights before using a shortcut, then convert your answer back to decimal as an independent check. Representation and value are different ideas.
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Digital Electronics