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DEMO: Binary and decimal

Worked examples

• $110_2 = 4 + 2 + 0 = 6$.
• $100_2 = 4$, because only the $4$s place is set.
• $13 = 8 + 4 + 1$, so $13 = 1101_2$.
• $111_2 = 4 + 2 + 1 = 7$.
• $10 = 8 + 2$, so $10 = 1010_2$.
• With $3$ bits the largest is $111_2 = 4 + 2 + 1 = 7$.

Key points

• Place values from the right are $1, 2, 4, 8$.
• Add the place values where the bit is $1$: $8 + 2 + 1$.
• Place values from the right are $1, 2, 4, 8, 16$.
• Only the fifth bit from the right is $1$.
• Write $25$ as a sum of powers of $2$.
• $25 = 16 + 8 + 1$.
• All five bits are $1$.
• $16 + 8 + 4 + 2 + 1$, or one less than $2^5$.
• Write $42$ as a sum of powers of $2$.
• $42 = 32 + 8 + 2$.
• The largest value has every bit set to $1$: $1111_2$.
• $8 + 4 + 2 + 1$.

Teacher video

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