[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