[Mathematic SPM] Number Bases

Source: ADaP

1. Which of the following are the numbers in base eight?
A. 1, 2, 3, 4, 5, 6, 7
B. 0, 1, 2, 3, 4, 5, 6, 7
C. 1, 2, 3, 4, 5, 6, 7, 8
D. 0, 1, 2, 3, 4, 5, 6, 7, 8

2. Which of the following is not the number in base five?
A. 2
B. 3
C. 4
D. 5

3. State, in base ten, the value of digit 2 in the number 2441₈
A. 100
B. 512
C. 1200
D. 1024

4. What is the value of the red digit of 1001101₂
A. 2⁵
B. 2⁷
C. 2⁶
D. 2⁸

5. The value of first digit 1 in 111000101₂
A. 102
B. 128
C. 225
D. 256

6. The expanded notation of 4352₈
A. 2 x 8³ + 5 x 8² + 3 x 8¹ + 4 x 8⁰
B. 2 x 8⁴ + 5 x 8³ + 3 x 8² + 4 x 8¹
C. 4 x 8³ + 3 x 8² + 5 x 8¹ + 2 x 8⁰
D. 4 x 8⁴ + 3 x 8³ + 5 x 8² + 2 x 8¹

7. State the number in base two for (1 x 2⁶) + (1 x 2⁵) + (1 x 2⁴) + (0 x 2³) + (0 x 2²)
+ (1 x 2¹) + ( 0 x 2⁰)
A. 1101011₂
B. 1101010₂
C. 1110010₂
D. 1110110₂

8. Express 10010011₂ as a number in base ten.
A. 136₁₀
B. 128₁₀
C. 147₁₀
D. 256₁₀

9. Express 1056₈ as a number in base ten.
A. 512₁₀
B. 524₁₀
C. 558₁₀
D. 568₁₀

10. Express 236₁₀ as a number in base two.
A. 100111₂
B. 1001111₂
C. 10011110₂
D. 11011101₂

11. Express 310₁₀ as a number in base five.
A. 2002₅
B. 2020₅
C. 2223₅
D. 2220₅

12. State the value of m and n for 34421₅ = 3 x 5^m + 4 x 5³ + 4 x 5² + 2 x 5ⁿ + 1 x 5⁰
A. m = 2, n = 1
B. m = 4, n = 1
C. m = 2, n = 0
D. m = 4, n = 0

13. Express 8³ + 8² + 8⁰ as a number in base eight.
A. 1101₈
B. 1015₈
C. 1055₈
D. 1450₈

14. Given that 2^x + 2¹ + 2⁰ = 100011₂, the value of x is
A. 5
B. 6
C. 7
D. 8

15. Given that 10011101₂ = y₁₀. The value of y is
A. 135
B. 129
C. 148
D. 157

16. Given that 11111010₂ = y₈, the value of y is
A. 761
B. 372
C. 552
D. 231

17. Given that 100₅ = m₂, the value of m is
A. 10111₂
B. 1100100₂
C. 11001₂
D. 1010101₂

18. Given that m9₁₀ = 344₅. The value of m is
A. 6
B. 7
C. 8
D. 9

19. Given that 214₈ = T₅. The value of T is
A. 1030
B. 1300
C. 1320
D. 1303

20. Express 2⁶ + 2³ + 2² + 1 as a number in base two.
A. 1100111₂
B. 1001010₂
C. 1101001₂
D. 1001101₂

21. Calculate the value of 110111₂ + 111011₂
A. 110010₂
B. 1110010₂
C. 1110110₂
D. 111110₂

22. 1011010₂ - 11101₂
A. 111101₂
B. 110101₂
C. 111000₂
D. 101101₂

23. Given that 1010₂ + m₂ = 11001₂, find the value of m.
A. 1011₂
B. 1110₂
C. 1101₂
D. 1111₂

24. Given that 10000₂ < x₂ < equiv="Content-Type" content="text/html; charset=utf-8">₂, the possible value of x is
A. 10001₂
B. 11110₂
C. 10011₂
D. 10010₂

25. Express 1101001₂ as a number in base eight.
A. 136
B. 115
C. 151
D. 321

26. Express 341₅ as a number in base eight
A. 100₈
B. 140₈
C. 155₈
D. 525₈

27. Given that x₂ = 125₈. The value of x is
A. 1101110₂
B. 1110001₂
C. 1010101₂
D. 1010110₂

28. Given that y₅ = 1001000110₂. The value of y is
A. 4312₅
B. 4431₅
C. 4004₅
D. 1234₅

29. Calculate the value of 110111₂ + 111011₂.
A. 110010₂
B. 1110010₂
C. 1110110₂
D. 111110₂

30. Given that 324_m = 131₈, so the value of m is
A. 2
B. 5
C. 8
D. 10