The 8-bit signed-magnitude representation of (−19)10 is:

Concept

In an n-bit signed-magnitude representation, the most significant bit stores the sign: 0 for positive and 1 for negative. The remaining n − 1 bits store the ordinary binary magnitude of the absolute value.

Application

1. Use 8 bits, so reserve the first bit for the sign and the remaining 7 bits for the magnitude.

2. Because the number is negative, the sign bit is 1.

3. Convert the magnitude: 19 = 16 + 2 + 1, so 1910 = 100112. Pad it to 7 bits: 0010011.

4. Join the sign bit and magnitude: 1 | 0010011 = 10010011.

Cross-check

Reading 10010011 as signed magnitude gives sign bit 1 (negative) and magnitude 00100112 = 1910, so it decodes back to −19.

Therefore, the 8-bit signed-magnitude representation is 10010011.