By Robert Milne
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Additional info for A theory of programming language semantics, part A
To change an octal number into a binary number, simply change each digit to binary reading from the right and write down the binary numbers in order. Quickly try the following: Check 5 1 Change the following numbers into binary: (a)48 (b)86 (c)l7 (d)l496 (e)212 3 (f)543 6 (g) 76 8 (h) 134 8 . 2 Change the following binary numbers into octal numbers: (a)lOll (b)lOlll (c)ll011011 (d)1010101. 5 Manipulation in Different Bases Some knowledge of addition, multiplication etc. is assumed. The following example should clarify any problems.
1 Directed Numbers There is always great confusion between the concept of a directed number, and the operations of addition and subtraction. The author will try to make it clearer or in this section by writing all numbers negative or positive like (a) Addition @ @= @ @+@=@ @+@=@ @ @. + Addition of any negative number to any other number always gives a smaller answer. Addition of any positive number to any other number always gives a larger This is only helpful advice; the student still has to get the answer right!
Check4 The following numbers should be converted into denary to refresh your mind: (a) 136 8 (f) 100011 2 (b) 2148 (c) 2150 8 (d) 1011 2 (e) 1111012 (h)2415 6 (i)6135 7 (j)33333s . 3 (a) Change 683 into binary. (b) Change 63 8 into base 3 . (c) Change 1011101 2 into base 8 (often referred to as octal). Solution The method usually involves a continuous division process writing down the remainders. __ _ __ Read upwards for the answer this number is zero :. 683 = 1010101011 2. 21 (b) If changing from one base to another, usually you have to go via base 10.
A theory of programming language semantics, part A by Robert Milne