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For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands.
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
Mode 3/A is often combined with Mode C to provide altitude information as well. [2] C: Provides the aircraft's pressure altitude and is usually combined with Mode 3/A to provide a combination of a 4-digit octal code and altitude as Mode 3 A/C, often referred to as Mode A and C [2] 4: Provides a 3-pulse reply, delay is based on the encrypted ...
For each of them, compute the remainder by 4 (the second largest modulus) until getting a number congruent to 3 modulo 4. Then one can proceed by adding 20 = 5 × 4 at each step, and computing only the remainders by 3. This gives 4 mod 4 → 0. Continue 4 + 5 = 9 mod 4 →1. Continue 9 + 5 = 14 mod 4 → 2. Continue 14 + 5 = 19 mod 4 → 3.
Even without knowledge that we are working in the multiplicative group of integers modulo n, we can show that a actually has an order by noting that the powers of a can only take a finite number of different values modulo n, so according to the pigeonhole principle there must be two powers, say s and t and without loss of generality s > t, such that a s ≡ a t (mod n).
Developed by the US Navy, this pod is fitted with the Mk 11 Mod 5 20 mm cannon, along with 750 rounds of ammunition. [20] This pod is said to have been used on a variety of US Navy and Marine Corps aircraft including the A-4 Skyhawk, F-4 Phantom II, A-7 Corsair II, and OV-10 Bronco. [1]
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Mode 3/A: military/civilian; provides a 4-digit octal (12 bit) identification code for the aircraft, assigned by the air traffic controller. Commonly referred to as a squawk code. [21] Mode 4: military only; provides a 3-pulse reply, delay is based on the encrypted challenge. [21]