Concept

How do place values and counting work in binary?

Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1

"The rules for interpreting place value are the same: 110101₂ = 1 × 2⁵ + 1 × 2⁴ + 0 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰ = 1 × 32 + 1 × 16 + 0 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 53₁₀. So in binary we have a one’s-place, a two’s-place, a four’s-place, an eight’s-place, and so on. We call the right-most place the least significant bit (LSB) and the left-most the most significant bit (MSB). Counting up from zero is really just the same as any other base, although it feels a little strange in binary because you “roll over” so often: 0₂ is zero, 1₂ is one, 10₂ is two, 11₂ is three, 100₂ is four, 101₂ is five, 110₂ is six, 111₂ is seven, 1000₂ is eight, and 1001₂ is nine."

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How do place values and counting work in binary? | Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk | Bifalgorithm | Bifalgorithm