Binary Numbers - AP Computer Science Principles

1. Define a nibble in terms of binary numbers.

   A nibble is 4 bits. Half a byte, convenient for hex digit representation.

2. What is the binary subtraction of 1111 - 1101?

   10. Subtract column by column: $1111 - 1101 = 10$.

3. Convert the binary number 1010 to hexadecimal.

   A. Binary 1010 equals decimal 10, which is hex A.

4. What does the binary number 111 equal in octal?

   7. Binary 111 equals decimal 7, which is octal 7.

5. What is the binary equivalent of the decimal number 3?

   11. Decimal 3 = $2 + 1 = 2^1 + 2^0$, so positions 1 and 0 are set.

6. Define a bit in the context of binary numbers.

   A bit is a binary digit, 0 or 1. The fundamental unit of binary information.

7. How is the number zero represented in binary?

   0. Zero has no set bits in any position.

8. What is the binary subtraction of 1010 - 101?

   101. Subtract column by column: $1010 - 101 = 101$.

9. Convert the binary number 100 to hexadecimal.

   4. Binary 100 equals decimal 4, which is hex 4.

10. Convert the binary number 1100 to decimal.

    12. Binary 1100 = $8 + 4 = 2^3 + 2^2 = 12$.

11. What does the binary number 1001 equal in octal?

    11. Binary 1001 equals decimal 9, which is octal 11.

12. What is the result of binary multiplication: 101 * 11?

    1111. Binary multiplication: $101 \times 11 = 5 \times 3 = 15 = 1111$.

13. Convert the binary number 111 to decimal.

    7. Binary 111 = $4 + 2 + 1 = 2^2 + 2^1 + 2^0 = 7$.

14. Convert the decimal number 4 to binary.

    100. Decimal 4 = $2^2$, so only position 2 is set.

15. What is the binary subtraction of 1101 - 101?

    1000. Subtract column by column: $1101 - 101 = 1000$.

16. What is the result of binary multiplication: 10 * 10?

    100. Binary multiplication: $10 \times 10 = 2 \times 2 = 4 = 100$.

17. What is the binary equivalent of the decimal number 7?

    111. Decimal 7 = $4 + 2 + 1 = 2^2 + 2^1 + 2^0$.

18. What is the binary addition of 110 + 1011?

    10001. Add column by column with carry: $110 + 1011 = 10001$.

19. How many bits are in a byte?

    8 bits. Standard computer storage unit containing 8 binary digits.

20. Convert the decimal number 8 to binary.

    1000. Decimal 8 = $2^3$, so only position 3 is set.

21. What is the binary equivalent of the decimal number 9?

    1001. Decimal 9 = $8 + 1 = 2^3 + 2^0$, so positions 3 and 0 are set.

22. What does the binary number 1111 equal in octal?

    17. Binary 1111 equals decimal 15, which is octal 17.

23. What is the result of binary addition: 1011 + 110?

    10001. Add column by column with carry: $1011 + 110 = 10001$.

24. What is the binary subtraction of 1100 - 101?

    111. Subtract column by column with borrowing: $1100 - 101 = 111$.

25. What is the binary representation of the hexadecimal number A?

    1010. Hex A equals decimal 10 = $8 + 2 = 2^3 + 2^1$.

26. What is the largest number that can be represented with 4 bits?

    15. With 4 bits, maximum is $2^4 - 1 = 16 - 1 = 15$.

27. What is the binary equivalent of the decimal number 10?

    1010. Decimal 10 = $8 + 2 = 2^3 + 2^1$, so positions 3 and 1 are set.

28. Convert the binary number 101 to hexadecimal.

    5. Binary 101 equals decimal 5, which is hex 5.

29. Convert the binary number 1101 to decimal.

    13. Binary 1101 = $8 + 4 + 1 = 2^3 + 2^2 + 2^0 = 13$.

30. What is the result of binary multiplication: 11 * 11?

    1001. Binary multiplication: $11 \times 11 = 3 \times 3 = 9 = 1001$.

31. Convert the decimal number 15 to binary.

    1111. Decimal 15 = $8 + 4 + 2 + 1$, all four low-order bits set.

32. Convert the decimal number 6 to binary.

    110. Decimal 6 = $4 + 2 = 2^2 + 2^1$, so positions 2 and 1 are set.

33. Convert the binary number 1011 to decimal.

    11. Binary 1011 = $8 + 2 + 1 = 2^3 + 2^1 + 2^0 = 11$.

34. What does the binary number 110 equal in octal?

    6. Binary 110 equals decimal 6, which is octal 6.

35. What is the binary representation of the decimal number 5?

    101. Decimal 5 = $4 + 1 = 2^2 + 2^0$, so positions 2 and 0 are set.

36. What is the binary addition of 1001 + 101?

    1110. Add column by column: $1001 + 101 = 1110$.

37. What is the binary representation of the hexadecimal number F?

    1111. Hex F equals decimal 15, all four low-order bits set.

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