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Converting from binary to denary

When converting binary numbers, always jot down the 'worth' of each bit position. It will really help you avoid mistakes. Usually, jotting down the bit positons for a single byte is sufficient, but you could add even more bit positions if you needed to.

Example 1
Convert 0110 into a denary number.

Looking at the table above, 0110 = (0 * 8) + (1 * 4) + (1 * 2) + (0 * 1) = 0 + 4 + 2 + 0 = 6

Example 2
Convert 100110 into a denary number.

Looking at the table above, 100110 = (1 * 32) + (0 * 16) + (0 * 8) + (1 * 4) + (1 * 2) + (0 * 1) = 32 + 0 + 0 + 4 + 2 + 0 = 38

Example 3
Convert 100110 into a denary number.

Looking at the table above, 0100 1000 = (0 * 128) + (1 * 64) + (0 * 32) + (0 * 16) + (1 * 8) + (0 * 4) + (0 * 2) + (0 * 1) = 0 + 64 + 0 + 0 + 8 + 0 + 0 + 0 = 72

Convert the following into denary without a calculator. When you have done as many as you can, check your answers against the answers of someone sitting next to you. Then check your answers using a calculator or an onine converter.

Q1. 011
Q2. 101
Q3. 1000
Q4. 0010
Q5. 01101
Q6. 11111
Q7. 10101
Q8. 101111
Q9. 000110
Q10. 101010
Q11. 000001
Q12. 1011111
Q13. 1001011
Q14. 1011 1111
Q15. 0000 1110
Q16. 0101 0101
Q17. 0111 0100
Q18. 1000 0000
Q19. 1001 0111
Q20. 1111 1111

Extension questions
Q21. 0001 0110 0000
Q22. 0010 0000 0011
Q23. 0101 0001 0100
Q24. 0111 1111 1110
Q25. 1111 1111 1111 1100

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