Mastering Mathematics for Electrical and Electronic by Noel M. Morris (auth.)

By Noel M. Morris (auth.)

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Sample text

Thus in the octal system the 8th value is 7s +Is = lOs = (I X 8 1) + (0 X 8°) The above number should be stated as 'one, zero in octal' and NOT as 'ten octal', simply because the use of 'ten' is restricted to the decimal system. The next higher octal value is lis, and the sixteenth number is 20s = (2 X 8 1) + (0 X 8°). In every numbering system, we must assign a character to each value. Thus, in the hexadecimal system, we assign the character 'a' to the lOth value, 'b' to the II th value, and so on up to the 15th which is 'f.

9 Binary coded decimal codes Whilst electronic systems deal most easily with binary numbers, mankind prefers decimal codes. By coding decimal numbers in binary form, suitable numbering systems can be devised which are acceptable to both man and machine alike. Such coding systems are known as binary-coded decimal codes (BCD codes). 1 uses four bits to convey the ten decimal digits 0-9. There are, in fact, more than 29 000 million possible 4-bit codes we can use. Of these, 70 have weighted codes, 17 of them have positive weights, and others have negative weights.

The 1 's complement representation of a binary number is obtained as follows Change the O's into l's, and the 1's into O's throughout the number. The 2's complement representation of a binary number is obtained by either of the following methods 1. Form the l's complement of the number, and add '1' to the least significant bit of the number so formed. 2. Copy the number (commencing at the lsb) up to and including the least significant '1'; thereafter, change all the 1's into O's and O's into 1's.

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