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Binary Numbers: Exercises

Print this page and answer the questions. Choose any 20 questions from the 33
listed. The harder the questions you choose the higher your potential mark.
Maximum mark is (1 * 6) + (6 * 3) + (3 * 2) = 30. Question 3 counts as one
question.

Name:

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1. Conversion From Binary to Denary

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a. 4 Bit Binary (1 mark each)

0110

1011

1110

0111

1100

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b. 8 Bit Binary (2 marks each)

00010001

00011000

00010011

00100011

00101010

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c. Harder 8 Bit Binary (3 marks each)

00111000

00111100

00111110

01100001

11011011

11101011

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Conversion From Denary to Binary

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a. Easy (1 mark each)

12

65

128

96

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b. Harder (2 marks each)

101

231

247

219

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3. Patterns

a. Write down the sequence of powers of 2 up to 2^8 (1 mark)

b. Write down the sequence of the largest numbers that can be represented in n
bits (largest number in 1 bit, largest number in 2 bits, 3 bits, etc. (2 marks)

c. What is the connection between these two sequences? Can you express them in a
formula? (3 marks)

Sequence of powers is:

Sequence of largest numbers in n bits is:

Formula: