Data Representation -Binary Conversions

1. L.P. I can write numbers in binary.
We can split the number 327 into 3 hundreds + 2 tens + 7 units.
There are ten units in a ten, ten tens in a hundred, ten hundreds in a thousand and so on: each digit in the number is
worth ten times more or ten times less than the digits on each side - so in the number 1,111 the four digits are the same,
but they represent one thousand (ten hundreds), one hundred (ten tens), one ten (ten units) and one unit (ten tenths).
This is called base ten. We use this for normal numbers because we have ten fingers and thumbs so ten is a useful
number for counting.
Computers don’t have fingers and they don’t have thumbs.
They don’t use base ten. Instead they use base two.
This means each digit in a number is either twice or half the value of the digits next to it. Instead of thousands,
hundreds, tens and units, a computer has eights, fours, twos and units.
In base ten, we use ten different digits: 0,1,2,3,4,5,6,7,8 and 9. In base two, the computer only needs two different
digits: 0 & 1.
The number 1111 in base two is the number 15 in base ten. Can you see why?
1. Can you work out what these numbers in base two would be in normal base ten?
Eights
1
Fours
1
Twos
1
Units
1

2. a. 1010
b. 11
c. 1000
d. 1110
2. Can you work out what these numbers in base ten would be in base two?
a. 6
b. 13
c. 2
3. Remember that in base two, each digit is worth twice the digit to the right. Can you work out what 100000 is in
normal base ten?
4. We can write words in binary too. In base ten, a = 1, b = 2, c = 3, d = 4, e = 5, f = 6, g = 7, h = 8, i = 9, j = 10, k =
11, l = 12, m = 13, n = 14, o = 15, p = 16, q = 17, r = 18, s = 19, t = 20, u = 21, v = 22, w = 23, x = 24, y = 25, z =
26. 14 in base ten is 1110 in base two. This means we can write 1110 instead of the letter n (n=14). Can you
work out whose name this is in base two?
00100 01111 00011 10100 01111 10010 10111 01000 01111
5. Can you translate and solve this riddle?
Eights
0
Fours
0
Twos
0
Units
0
0
1

3. 00111 01001 10110 00101 01101 00101 00110 01111 01111 00100 00001 01110 00100 01001
10111 01001 01100 01100 01100 01001 10110 00101; 00111 01001 10110 00101 01101 00101
10111 00001 10100 00011 10010 00001 01110 00100 01001 10111 01001 01100 01100 00100
01001 00101. 10111 01000 00001 10100 00001 01101 01001?
The answer is written below. However, it is written in hexadecimal, which is base sixteen. Base ten uses ten different
digits (including 0), base two uses two different digits (0 and 1), so base sixteen uses sixteen different digits: 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, C, D, E, F
The number 300 in base ten, for example, is 12C in hexadecimal, base sixteen.
Anyway, here is the answer to the riddle:
06 09 12 05
Two-hundred-and-fifty-sixes
0
Sixteens
1
Units
7
In hexadecimal, 17 means
23 in base ten because
there is one 16 and 7 units.