What is the minimum decimal value (negative value) represented by an 8-bit signed binary number with a 4-bit fraction?

Question

What is the minimum decimal value (negative value) represented by an 8-bit signed binary number with a 4-bit fraction?

Answer 1

8 bits for signed Binary

1 Bit used for Sign.

4 Bits used for Fraction

Since we are looking for largest negative number, the first bit is set to 1, 2-8 are also set to 1.

The integer number would be 1 * 2⁰ + 1 * 2¹ + 1 * 2² = 7

The fraction would be 1 * 2^-1 + 1 * 2^-2 + 1 * 2^-3 + 1 * 2^-4 = 0.9375

Therefore the largest negative value would be -7.9375