need to create a number system using only: A=1, B=2, C=3, D=4 and Zero=0. Help
0
1
2
3
4
1 0 = 5 = 5^1 + 0
1 1 = 6 = 5^1 + 1
1 2 = 7 = 5^1 + 2
1 3 = 8
1 4 = 9
2 0 = 10 = 2*5^1 + 0 *5^0
2 1 = 11 = 2*5^1 + 1 *5^0
2 2 = 12 = 2*5^1 + 2 *5^0
etc
...
2 3 1 = 70 = 2*5^2 + 3*5^1 + 1*5^0
Now put in A for 1, B for 2, C for 3 etc
so for example
2 3 1 is B C A
2 3 1 = 66 = 2*5^2 + 3*5^1 + 1*5^0
Now put in A for 1, B for 2, C for 3 etc
so for example
2 3 1 is B C A
To create a number system using the given characters (A, B, C, D, and Zero), we can assign each character a numerical value and establish some rules for writing and calculating numbers.
Here is how you can create the number system:
1. Assign numerical values to each character:
- A = 1
- B = 2
- C = 3
- D = 4
- Zero = 0
2. Write numbers using the assigned characters:
- For example, the number "2" can be represented as "B" since B is assigned the value of 2.
3. Use place value:
- Just like in our decimal system (base-10 system), each position in the number represents a specific value based on the place value.
- In our case, the positions can be defined as follows: A for ones place, B for tens place, C for hundreds place, D for thousands place, and so on.
4. Addition and Subtraction:
- To perform addition and subtraction, you can simply replace the characters with their numerical values and carry out the operations accordingly.
- For example, to add "CAB" and "BB":
- CAB = 321 (C = 3, A = 1, B = 2)
- BB = 22 (B = 2)
- 321 + 22 = 343 (replace the numerical values with characters: CDC)
- So, CAB + BB = CDC
5. Multiplication and Division:
- To perform multiplication and division, you can follow similar rules as in the decimal system by using the numerical values assigned to the characters.
- For example, to multiply "DA" by "B":
- DA = 41 (D = 4, A = 1)
- B = 2
- 41 * 2 = 82 (replace the numerical value with the character: BB)
- So, DA * B = BB
By following these steps, you can create and work with a number system using the characters A, B, C, D, and Zero.