The number 75 in the decimal system when expressed in the number system to the base 7, comprises
Answers
Answer:
input 1 base-10
output 1 base-7
Answer:
Step-by-step explanation:
A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number and the maximum numbers that can be written with the given number of digits.
The Binary Number System: The binary number system with only two independent digits, 0 and 1, is a base-2 number system. All larger binary numbers are represented in terms of ‘0’ and ‘1’.
Decimal to Binary Conversion:
Step 1: Divide 75 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.
75 / 2 = 37 with 1 remainder
Step 2: Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.
37 / 2 = 18 with 1 remainder
Step 3: Repeat Step 2 above until the Whole part is 0.
18 / 2 = 9 with 0 remainder
9 / 2 = 4 with 1 remainder
4 / 2 = 2 with 0 remainder
2 / 2 = 1 with 0 remainder
1 / 2 = 0 with 1 remainder
Step 4: Write down the Remainders in reverse order to get the answer to 75 as a binary.
When we put the remainders together in reverse order, we get the answer 1001011
Hence, the binary equivalent of decimal number 75 is 1001011
NOTE:
The decimal number system has a base of 10 as it has 10 independent digits, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The octal and hexadecimal number systems have a radix (or base) of 8 and 16, respectively.