Number System Conversion

1. What is the core rule to convert a decimal integer to another system?

   (a) Divide by base (b) Multiply by base (c) Add 1 (d) Subtract 1

   Answer: a

2. What is the rule to convert a decimal fraction to another number system?

   (a) Divide by base (b) Multiply by base (c) Divide by 2 (d) Multiply by 8

   Answer: b

3. What is the equivalent binary value of the decimal number $(25)_{10}$?

   (a) 11001 (b) 10101 (c) 11100 (d) 10011

   Answer: a

4. What is the equivalent octal value of the decimal number $(30)_{10}$?

   (a) $(36)_8$ (b) $(35)_8$ (c) $(37)_8$ (d) $(40)_8$

   Answer: a

5. Which is the hexadecimal form of the decimal number $(42)_{10}$?

   (a) 2A (b) 2B (c) 3A (d) 4A

   Answer: a

6. What is the general rule to convert any system to decimal?

   (a) Multiply place value (b) Divide by base (c) Direct addition (d) Multiply by 2

   Answer: a

7. What is the equivalent decimal value of the binary number 1101?

   (a) 11 (b) 12 (c) 13 (d) 14

   Answer: c

8. What is the equivalent decimal value of the octal number $(25)_8$?

   (a) 20 (b) 21 (c) 22 (d) 23

   Answer: b

9. What is the equivalent decimal value of the hexadecimal number $(1A)_{16}$?

   (a) 26 (b) 27 (c) 28 (d) 29

   Answer: a

10. What is the decimal value of the base-5 number $(12)_5$?

    (a) 7 (b) 8 (c) 9 (d) 10

    Answer: a

Binary Addition & Subtraction

11. In binary addition, what is $1 + 1$?

    (a) 0 (b) 1 (c) 10 (d) 11

    Answer: c

12. In binary addition, what is $1 + 1 + 1$?

    (a) 10 (b) 11 (c) 0 (d) 1

    Answer: b

13. What is the binary sum of 101 and 011?

    (a) 1000 (b) 110 (c) 111 (d) 101

    Answer: a

14. In binary subtraction, what is $1 - 1$?

    (a) 0 (b) 1 (c) 10 (d) 11

    Answer: a

15. In binary subtraction, what is the Borrow when $0 - 1$ occurs?

    (a) 0 (b) 1 (c) 2 (d) 10

    Answer: b

16. What will be the result of subtracting 011 from 110?

    (a) 001 (b) 011 (c) 100 (d) 010

    Answer: b

17. What remains when 00001 is subtracted from 1000?

    (a) 111 (b) 110 (c) 101 (d) 011

    Answer: a

18. Where is the Carry bit added in binary addition?

    (a) Left column (b) Right column (c) Not added (d) Directly at end

    Answer: a

19. What is obtained by adding 1 to the binary number 111?

    (a) 1000 (b) 1111 (c) 100 (d) 110

    Answer: a

20. What is the decimal value of the binary subtraction result 101?

    (a) 4 (b) 5 (c) 6 (d) 7

    Answer: b

Octal Addition & Subtraction

21. In the octal number system, what is $7 + 1$?

    (a) 8 (b) 9 (c) 10 (d) 11

    Answer: c

22. In octal addition, what is $(5)_8 + (4)_8$?

    (a) $(9)_8$ (b) $(11)_8$ (c) $(10)_8$ (d) $(12)_8$

    Answer: b

23. What is the sum of the octal numbers $(16)_8$ and $(4)_8$?

    (a) $(20)_8$ (b) $(22)_8$ (c) $(24)_8$ (d) $(12)_8$

    Answer: b

24. How much must be borrowed in octal subtraction if the upper digit is smaller?

    (a) 2 (b) 8 (c) 10 (d) 16

    Answer: b

25. In the octal system, what is $(10)_8 - (1)_8$?

    (a) 7 (b) 9 (c) 8 (d) 6

    Answer: a

26. In the octal system, what is $(42)_8 - (5)_8$?

    (a) $(37)_8$ (b) $(35)_8$ (c) $(36)_8$ (d) $(34)_8$

    Answer: b

27. What is the decimal value of the octal sum $(20)_8$?

    (a) 16 (b) 17 (c) 18 (d) 20

    Answer: a

28. In the octal system, what is $7 + 7$?

    (a) $(14)_8$ (b) $(16)_8$ (c) $(12)_8$ (d) $(10)_8$

    Answer: b

Hexadecimal Addition & Subtraction

29. In the hexadecimal number system, what is $F + 1$?

    (a) G (b) 10 (c) 16 (d) 20

    Answer: b

30. In hexadecimal addition, what is $A + B$?

    (a) 21 (b) 15 (c) C (d) F

    Answer: b

31. In the hexadecimal system, what is $(9)_{16} + (7)_{16}$?

    (a) $(16)_{16}$ (b) $(10)_{16}$ (c) $(F)_{16}$ (d) $(11)_{16}$

    Answer: b

32. What will be the result of adding 1 to $(9A)_{16}$?

    (a) $(9B)_{16}$ (b) $(A0)_{16}$ (c) $(99)_{16}$ (d) $(AA)_{16}$

    Answer: a

33. What value is taken as Borrow in hexadecimal subtraction?

    (a) 2 (b) 8 (c) 10 (d) 16

    Answer: d

34. In the hexadecimal system, what is $(10)_{16} - (1)_{16}$?

    (a) F (b) 9 (c) E (d) A

    Answer: a

35. In the hexadecimal system, what is $(20)_{16} - (A)_{16}$?

    (a) $(1A)_{16}$ (b) $(16)_{16}$ (c) $(1F)_{16}$ (d) $(10)_{16}$

    Answer: a

36. What is $F - F$?

    (a) 0 (b) 1 (c) E (d) 10

    Answer: a

37. What is the decimal value of the hexadecimal sum $(10)_{16}$?

    (a) 10 (b) 16 (c) 15 (d) 20

    Answer: b

38. In the hexadecimal system, what is $E + 2$?

    (a) 16 (b) 10 (c) F (d) 11

    Answer: b

39. What is the immediate next number of $(FF)_{16}$?

    (a) $(100)_{16}$ (b) $(GG)_{16}$ (c) $(FE)_{16}$ (d) $(200)_{16}$

    Answer: a

40. What is the result of subtracting 5 from the hexadecimal value $(A)_{16}$?

    (a) 5 (b) 4 (c) 6 (d) 3

    Answer: a