What decimal value does the 8 bit binary number 00010001 have?

The 8-bit binary number 00010001 can be interpreted in different ways depending on the number system used. Let’s analyze it in three cases:

1. Unsigned Number:

   When interpreting 00010001 as an unsigned number, we simply convert it to decimal by calculating the powers of 2. Each position from right to left represents 2 raised to the power of that position’s index (starting from 0). For 00010001, this calculation is:

   0 * 2^7 + 0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 0 + 0 + 0 + 16 + 0 + 0 + 2 + 1 = 17

   Thus, in unsigned representation, 00010001 equals 17.

2. Signed Magnitude Representation:

   In signed magnitude representation, the first bit indicates the sign (0 for positive, 1 for negative), while the remaining bits represent the magnitude. Since the first bit of 00010001 is 0, it is a positive number. The magnitude derived from the remaining bits (0010001) is calculated the same way as before:

   0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 0 + 0 + 16 + 0 + 0 + 2 + 1 = 17

   Therefore, interpreted as signed magnitude, 00010001 is also 17.

3. Two’s Complement Representation:

   In two’s complement, if the first bit is 0, the value is the same as in unsigned representation, meaning it is positive. Therefore, 00010001 retains the same value:

   0 * 2^7 + 0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 17

   So, in the two’s complement system, 00010001 also equals 17.

In summary, regardless of whether it’s interpreted as an unsigned number or in signed magnitude and two’s complement representations, the 8-bit binary number 00010001 corresponds to the decimal value 17.