HL Homework: Number representation

This homework covers the following points from the syllabus:

  • 3.5.3 Express numbers in the bases: decimal, binary and hexadecimal
  • 3.5.4 Convert integers between the bases specified in 3.5.3 (maximum 8 bits).
  • 3.5.5 Apply binary notation to represent integers, both positive and negative, using the method-of-two’s complement.
  • 4.1.1 Calculate in the bases specified in 3.5.3. For binary and hexadecimal calculations, only addition is required

Please put this homework in my dropbox by 6am on the morning of Wednesday 17th August. You can do it on paper if you like, but if you do you must scan it or take a clear digital photo of it and put it in my dropbox. Make sure the filename includes your name please.


1. Convert the following numbers to (a) binary and (b) hexadecimal:

a. 15
b. 64
c. 255
d. 329

2. It is very easy to convert from hexadecimal to binary and vice versa. Explain briefly how to convert from hexadecimal to binary.

3. Convert the following binary numbers to decimal:

(a) 1000
(b) 10110
(c) 11100
(d) 11110101

4. Convert the following hex numbers to decimal:

(a) 10
(b) 8C
(c) 128
(d) 1AF

5. Use 8-bit two’s complement to represent the following decimal numbers:

(a) 56
(b) -4
(c) -127
(d) 0

6. Calculate the following sum in hexadecimal: 68 + CA.

7. Using 5-bit two’s complement, state (a) the maximum integer that can be stored, and (b) the value of the minimum integer that can be stored.

8. Briefly explain why two’s complement is more effective than using (a) a sign bit or (b) one’s complement.

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