Number Bases
Convert numbers between base 10 (denary) and other bases.
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Why Do We Use Bases?
We usually count with base 10 (denary) because we have ten fingers. But computers use base 2 (binary), and some systems use base 8 (octal) or base 16.
Key idea: In base b, each place value is a power of b. The digits allowed are 0 up to b−1.
Converting Base 10 to Base 2
Divide by 2 and keep the remainders. Read the remainders from last to first.
Convert 6 to binary: 6 ÷ 2 = 3 remainder 0; 3 ÷ 2 = 1 remainder 1; 1 ÷ 2 = 0 remainder 1. Reading bottom-up: 110₂.
Converting Base 2 to Base 10
Convert 101₂ to denary: 101₂ = 1×2² + 0×2¹ + 1×2⁰ = 4 + 0 + 1 = 5.
Practice
Try: (1) Convert 10 to binary. (2) Convert 1100₂ to denary. Write out all your steps.
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