Binary 6 – Assorted problems
Name: __________________________
Criteria 5
1. Convert the following Decimal numbers to unsigned Binary
a) 24
b) 251
2. Convert the following unsigned Binary numbers to Decimal
a) 11010
b) 1010101
3. Perform the following arithmetic calculations, using unsigned binary.
a) 01101
b) 01001
c) 01111
+ 01011
+ 0100
+
1
-----------------------------------
4. Using unsigned binary convert the following decimal numbers to binary
a) 59
b) 98
c) 131
5. Convert these decimal numbers to binary using an 8-bit two’s complement
representation. (Hint: Take the two’s complement of your answers from Q4)
a) -59
b) -98
c) -131
Rosny College 2012, adapted by Claremont College 2014
Page 1 of 4
6. Perform the following calculations, in binary, using two’s complement where
necessary
a)
3
b)
4
c)
6
+ 4
- 4
-3
-------------------
7. In Two’s Complement arithmetic, explain what is meant by, and how we deal with:
a) ‘Overflow’
b) ‘Carry out’
8. Convert the following binary numbers to decimal, using 8-bit binary floating point
representation (with 1 bit for the sign, 3 bits for the exponent in two’s complement,
and 4 bits for the mantissa).
a) 1 001 1101
sign =
exponent =
mantissa =
number =
b) 0 111 1010
sign =
exponent =
mantissa =
number =
9. Convert the following numbers to binary, using the floating point representation
described in the previous question.
a) 1.75
b) -0.4
Rosny College 2012, adapted by Claremont College 2014
Page 2 of 4
10. Calculate the following file sizes in kilobytes:
a) A funky black and white photograph has been taken on
an iPhone.
It is a surprisingly large image that is square, 1936
pixels each side and uses 32 colours.
b) When adding a soundtrack to a YouTube clip, before uploading, you need to
consider the size of the music file and how it will affect the overall movie clip size.
You have a great soundtrack you would like to use. It goes for a minute and
thirteen seconds. It was sampled at 16kHz using 24bit audio.
c) The Portable Network Graphics (PNG) file type gives the user a range of options
for storing an image. The PNG file is made up of sets of data called chunks. The
main IDAT chunk stores the data on each pixel in the image. The data in the
PLETE chunk is a colour palette and will be included in the file if needed. The
PLETE chunk has a maximum of 256 entries made up of 3 bytes (one byte for
red, one for green and one for blue).
8-bit Truecolour
One option for storing the image is 8-bit Truecolour which stores all the data in
the IDAT chunk. Each pixel is represented by 3 bytes (one byte for red, one for
green and one for blue).
Rosny College 2012, adapted by Claremont College 2014
Page 3 of 4
eg. Using 8-bit Truecolour, the data in the IDAT chunk for a four-pixel file would
be:
red byte
blue byte
green byte
37
44
98
230
2
12
230
2
12
45
120
32
8-bit Indexed-colour
Another option for storing the image is 8-bit Indexed-colour which stores data
using the IDAT and PLETE chunks. The PLETE chunk stores an entry for each
colour used by the image. In the IDAT chunk each pixel is represented by the
entry number from the PLETE chunk corresponding to the colour of that pixel.
eg. Using 8-bit Indexed-colour, the data in the PLETE chunk for three colours
would be:
red byte
blue byte
green byte
37
44
98
230
2
12
45
120
32
The corresponding data in the IDAT chunk for 8-bit Indexed-colour for four pixels
would be:
index byte
0
1
1
2
A user wishes to store a 290-pixel image that has 200 different colours. Explain,
showing your calculations, that it would take less space to store the image using
8-bit Truecolour than using 8-bit Indexed-colour.
Rosny College 2012, adapted by Claremont College 2014
Page 4 of 4