Negative numbers in all number systems can be represented in complementary form. For any number system there exist two types of complements and they are:
- Base complement
- (Base-1) complement
1. (Base-1) Complement Calculation :
To calculate (base-1) complement of a given number we have to subtract each and every digit from (base-1) value. That is, if base or radix of a number is “x” then to find the (base-1) complement of that number we have to subtract each and every digit from (x-1).
Example: Calculate the 8’s complement of the base 9 number -6350.
If 9 is the base, then (base-1) value is 8. Therefore 8's complement is: 8888-6350 = 2538
2. Base Complement Calculation :
Method I
To calculate the base complement of a given number proceeds as follows:
- Step 1: Scan the number from the right side and copy all leading zeros until the first non-zero digit is encountered.
- Step 2: Subtract the first non-zero digit from “base value” and the rest of the digits from “base-1 value”.
Example: Calculate the base complement of the base 9 number -6350.
Scanning from right the first non-zero digit is 5. Subtract 5 from 9 and the remaining digits from 8. 9-5 = 4 8-3 = 5 8-6 = 2 Therefore 9's complement of base 9 number -6350 is 2540.
Method II
- Step 1: Calculate (base-1) complement of the number.
- Step 2: Add 1 to the (base-1) complement value.
Example: Calculate the base-1 complement of the base 9 number -6350.
The 8's complement of -6350 is 2538. Therefore 9's complement of base 9 number -6350 is: 2538+1 = 2540
Practice Questions:
(1) Calculate base complement of base 4 number -12300.
(2) Calculate base complement of decimal number -198021.
(3) Calculate base complement of base 14 number -A13.
(4) Calculate base-1 complement of base 4 number -12300.
(5) Calculate base-1 complement of base 4 number -635.
Answers:
(1) 21100 (2) 801979 (3) 3CB (4) 21033 (5) 253
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