Binary Equivalence of 148

D

To determine the binary equivalence of 148, we need to convert the decimal value into binary form. The binary system is a base-2 system, which means it only uses two digits, 0 and 1, to represent numbers. Each digit in a binary number represents a power of 2, starting from the rightmost digit with 2^0, which is equal to 1, and doubling each time we move one position to the left.

To convert decimal 148 to binary, we need to divide it by 2 successively, writing down the remainder after each division. Then, we read the remainders in reverse order to get the binary number. We continue dividing until the quotient becomes 0.

Here are the steps:

1. Divide 148 by 2: 148 ÷ 2 = 74, remainder 0
2. Divide 74 by 2: 74 ÷ 2 = 37, remainder 0
3. Divide 37 by 2: 37 ÷ 2 = 18, remainder 1
4. Divide 18 by 2: 18 ÷ 2 = 9, remainder 0
5. Divide 9 by 2: 9 ÷ 2 = 4, remainder 1
6. Divide 4 by 2: 4 ÷ 2 = 2, remainder 0
7. Divide 2 by 2: 2 ÷ 2 = 1, remainder 0
8. Divide 1 by 2: 1 ÷ 2 = 0, remainder 1

Reading the remainders in reverse order from step 8 to step 1, we get the binary number:

10010100

Therefore, the binary equivalence of decimal 148 is option D, 10010100.