Theory question 101
Number Bases(a) Copy and complete the binary multiplication table
× | 10 | 11 | 100 | 101
10 | 100 | – | 1000 | –
11 | 110 | – | 1100 | –
100 | – | – | 10000 | 10100
(b) Convert 11.011two to a number in base ten
(c) Simplify (9.6 × 1018)/(0.24 × 105) and express your answer in the form P × 10m where 1 < P < 10 and m is an integer.
Show the model answer
Model answer
(a) Missing entries: 10 × 11 = 110; 10 × 101 = 1010; 11 × 11 = 1001; 11 × 101 = 1111; 100 × 10 = 1000; 100 × 11 = 1100.
(b) 11.011two = 1×2 + 1×1 + 0×½ + 1×¼ + 1×⅛ = 2 + 1 + 0.25 + 0.125 = 3.375.
(c) 9.6/0.24 = 40, so the value is 40 × 1018−5 = 40 × 1013 = 4 × 1014.
Explanation
Check each binary product by converting to base ten (e.g. 3 × 3 = 9 = 1001two).