QuestionConvert the decimal number 4025 to base 4.

Studdy Solution

STEP 1

Assumptions1. The number to be converted is4025 (in base10) . The base to which we are converting is base4

STEP 2

To convert a number from base10 to another base, we need to divide the number by the base and keep track of the remainders. The remainders will form the digits of the number in the new base. We start with dividing the number by the base.
$\frac{4025}{4}$

STEP 3

Perform the division operation.
$\frac{4025}{} =1006 \, remainder \,1$

STEP 4

The remainder1 is the rightmost digit (also known as the least significant digit) of the number in base4. Now, we continue the process with the quotient1006.
$\frac{1006}{4}$

STEP 5

Perform the division operation.
$\frac{100}{4} =251 \, remainder \,2$

STEP 6

The remainder2 is the next digit of the number in base4. We continue the process with the quotient251.
$\frac{251}{4}$

STEP 7

Perform the division operation.
$\frac{251}{4} =62 \, remainder \,3$

STEP 8

The remainder3 is the next digit of the number in base4. We continue the process with the quotient62.
$\frac{62}{4}$

STEP 9

Perform the division operation.
$\frac{62}{4} =15 \, remainder \,2$

STEP 10

The remainder2 is the next digit of the number in base4. We continue the process with the quotient15.
$\frac{15}{4}$

STEP 11

Perform the division operation.
$\frac{15}{4} =3 \, remainder \,3$

STEP 12

The remainder is the next digit of the number in base4. We continue the process with the quotient.
$\frac{}{4}$

STEP 13

Perform the division operation.
$\frac{3}{} =0 \, remainder \,3$

STEP 14

The remainder3 is the leftmost digit (also known as the most significant digit) of the number in base4. As the quotient is now0, we have finished the conversion process.

STEP 15

Combine all the remainders from right to left (from the first division to the last) to get the number in base4.
$4025_{10} =33221_{4}$ The number4025 in base10 is equal to33221 in base4.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms