To determine the value of the decimal number 955 in both quin (base-5) system and the binary (base-2) system, we can follow these steps:
### Convert 955 to Quin System (Base-5):
1. Start with the decimal number 955.
2. Divide the number by 5 and keep track of the remainder.
3. Continue dividing the quotient by 5 until you reach a quotient of 0, recording each remainder along the way.
Following this procedure:
- 955 ÷ 5 = 191 with a remainder of 0
- 191 ÷ 5 = 38 with a remainder of 1
- 38 ÷ 5 = 7 with a remainder of 3
- 7 ÷ 5 = 1 with a remainder of 2
- 1 ÷ 5 = 0 with a remainder of 1
Now, reading the remainders in reverse order gives us the quin system value: 12310.
### Convert 955 to Binary System (Base-2):
To convert 955 into binary, we follow similar steps but we divide by 2 instead of 5:
1. Start with the decimal number 955.
2. Divide the number by 2 and record the remainder.
3. Continue dividing the quotient by 2 until the quotient is 0, recording each remainder.
Following this procedure:
- 955 ÷ 2 = 477 with a remainder of 1
- 477 ÷ 2 = 238 with a remainder of 1
- 238 ÷ 2 = 119 with a remainder of 0
- 119 ÷ 2 = 59 with a remainder of 1
- 59 ÷ 2 = 29 with a remainder of 1
- 29 ÷ 2 = 14 with a remainder of 1
- 14 ÷ 2 = 7 with a remainder of 0
- 7 ÷ 2 = 3 with a remainder of 1
- 3 ÷ 2 = 1 with a remainder of 1
- 1 ÷ 2 = 0 with a remainder of 1
Reading the remainders in reverse order gives us the binary value: 1110111011.
So, the value of the decimal number 955 in the quin system is 12310, and in the binary system, it is 1110111011.
