Express the decimal number 23 as a binary number.
The decimal number 23 can be expressed as a binary number as 10111.
To convert the decimal number 23 to a binary number, follow these steps:
Step 1: Start by dividing 23 by 2.
23 ÷ 2 = 11 with a remainder of 1
Step 2: Write down the remainder obtained in Step 1 (1) as the rightmost digit of the binary number.
Step 3: Now, divide the quotient obtained in Step 1 (11) by 2.
11 ÷ 2 = 5 with a remainder of 1
Step 4: Again, write down the remainder obtained in Step 3 (1) as the next digit of the binary number.
Step 5: Repeat the process by dividing the new quotient (5) by 2.
5 ÷ 2 = 2 with a remainder of 1
Step 6: Write down the remainder obtained in Step 5 (1) as the next digit of the binary number.
Step 7: Continue the process by dividing the new quotient (2) by 2.
2 ÷ 2 = 1 with a remainder of 0
Step 8: Write down the remainder obtained in Step 7 (0) as the next digit of the binary number.
Step 9: Finally, divide the new quotient (1) by 2.
1 ÷ 2 = 0 with a remainder of 1
Step 10: Write down the remainder obtained in Step 9 (1) as the leftmost digit of the binary number.
Step 11: Arrange all the remainders obtained in reverse order to get the binary number.
Therefore, the decimal number 23 in binary is 10111.
To express a decimal number in binary form, you can use a process called division by 2.
Here's how you can convert the decimal number 23 into binary:
1. Start by dividing the decimal number by 2.
23 ÷ 2 = 11 (with a remainder of 1)
2. Write down the remainder (1), which represents the least significant bit (LSB) of the binary number.
3. Divide the quotient obtained in the previous step (11) by 2.
11 ÷ 2 = 5 (with a remainder of 1)
4. Write down the remainder (1) next to the previous remainder. This represents the next bit of the binary number.
5. Repeat the division process with the updated quotient (5).
5 ÷ 2 = 2 (with a remainder of 1)
6. Write down the remainder (1) next to the previous remainders.
7. Continue dividing the quotient (2) by 2.
2 ÷ 2 = 1 (with a remainder of 0)
8. Write down the remainder (0) next to the previous remainders.
9. Finally, divide the last quotient (1) by 2.
1 ÷ 2 = 0 (with a remainder of 1)
10. Write down the remainder (1) next to the previous remainders.
11. The binary representation of the decimal number 23 is obtained by reading the remainders from the last step to the first step, i.e., from bottom to top.
Therefore, 23 in binary form is 10111.