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CLASS: SS 1
TOPIC: Modular Arithmetic
CONTENT:
- Addition, Subtraction, Multiplication and Division operations in module arithmetic
- Application to daily life
ADDITION AND SUBTRACTION:
In modular arithmetic, addition and subtraction are symbolized by ⊕ and ⊖ respectively. In the table we enter only the remainders when a pair of elements in the ⊕ on the set {0,1,2,3,4} modulo 5
| ⊕ | 0 | 1 | 2 | 3 | 4 |
| 0 | 0 | 1 | 2 | 3 | 4 |
| 1 | 1 | 2 | 3 | 4 | 0 |
| 2 | 2 | 3 | 4 | 0 | 1 |
| 3 | 3 | 4 | 0 | 1 | 2 |
| 4 | 4 | 0 | 1 | 2 | 3 |
Addition ⊕ in mod 5
- Simplify Find 39 ⊕ 29(mod 6)
Solution: 39 ⊕ 29= 68
= (6×11+2)
= 2(mod 6)
- Calculate the following in the given moduli (a) 12Θ5(mod 4) (b) 38 Θ42(mod 7)
Solution: (a) 12Θ5 = 7
7 = 4 + 3
= 3(mod 4)
(b) 38 Θ 42 = 4
4 = 7 + 3
= 3(mod 7)
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