By John Bird
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Extra info for Basic Engineering Mathematics, Third Edition
Sample text
Further problems on conversion between denary and binary numbers via octal (Answers on page 254) In Problems 1 to 3, convert the denary numbers given to binary numbers, via octal. 1. (a) 343 (b) 572 (c) 1265 The integer part is repeatedly divided by 8, noting the remainder, giving: 2. 71875 3. 78125 8 5613 Remainder 8 701 8 87 5 8 10 7 8 1 2 0 1 4. e. 5 Hexadecimal numbers The complexity of computers requires higher order numbering systems such as octal (base 8) and hexadecimal (base 16) which are merely extensions of the binary system.
This type of error is known as a blunder. (v) An order of magnitude error is said to exist if incorrect positioning of the decimal point occurs after a calculation has been completed. (vi) Blunders and order of magnitude errors can be reduced by determining approximate values of calculations. Answers which do not seem feasible must be checked and the calculation must be repeated as necessary. 1 calculation. 1 50 ð 20 ð 120 be approximated to and then, by 60 ð 40 1 cancelling, 50 ð 20 ð 120 1 60 ð 40 21 21 D 50.
The marks for each question are shown in brackets at the end of each question. (b) 3 5. 65 ð 10 4. 1 Binary numbers Problem 2. The system of numbers in everyday use is the denary or decimal system of numbers, using the digits 0 to 9. It has ten different digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) and is said to have a radix or base of 10. The binary system of numbers has a radix of 2 and uses only the digits 0 and 1. e. 510 , the suffixes 2 and 10 denoting binary and denary systems of numbers respectively.