# Specification Journal 008 ```Specification Journal 008
3.5.2 Number bases
For this specification point the following areas are covered:
 Be familiar with the concept of a number base, in particular:
o Decimal (base 10)
o Binary (base 2)
 Convert between decimal, binary and hexadecimal number bases
 Be familiar with, and able to use hexadecimal as a short hand for binary and understand
why it is used this way.
1.1 Key terms to define
Write a detail definition of each term given below. Look into the technical aspects of each key
word.
Term
Decimals (Base 10)
Binary (Base 2)
16)
Definition
Questions to complete
1.2 Binary to decimal conversions
Convert the following numbers from binary to decimal - Show your workings and do not use a
calculator
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
111011010101
110111
10011001
111010001001
1101010100011
11001111011101
111001011
11101001
11000101
11100110
1.3 Decimal to binary conversion
Convert the following decimal numbers to binary – Show your workings and do not use a calculator.
1) 345
2) 34
3)
4)
5)
6)
7)
8)
9)
10)
7854
887
58
128
358
63
80
206
Convert the following numbers from decimal to hexadecimal via binary. Show your workings and do
not use a calculator
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
587
1045
462
45
240
429
2057
5827
105
78
Convert the following numbers from hexadecimal to decimal via binary. Show your workings and do
not use a calculator
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
E9
1F
F1
AB