What is the combined value of all place values in a full byte?

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A full byte consists of 8 bits, and each bit can represent a value of either 0 or 1. When calculating the combined value of all place values in a byte, we consider all possible values that can be represented by these bits.

The maximum value that can be represented by an 8-bit binary number is 11111111, which translates to decimal as follows:

  • Each bit position corresponds to a power of 2:

  • 1 (2^0)

  • 2 (2^1)

  • 4 (2^2)

  • 8 (2^3)

  • 16 (2^4)

  • 32 (2^5)

  • 64 (2^6)

  • 128 (2^7)

When you sum these values for all bits set to 1 in an 8-bit binary number, you get:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.

This total value of 255 represents the maximum integer value that can be stored in a byte, ranging from 0 (all bits off) to 255 (all bits on).

Therefore,

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