## Discrete Mathematics with Applications 4th Edition

$44_{10}$
$62_{10} = (32 + 16 + 8 + 4 + 2)_{10} = 111110_2 → 00111110$ $−18_{10} = −(16 + 2)_{10}= −10010_2 → 00010010 → 11101101 → 11101110$ Thus the 8-bit representations of 62 and −18 are 00111110 and 11101110 respectively. Adding the 8-bit representations gives . 0 0 1 1 1 1 1 0 +1 1 1 0 1 1 1 0 $============$ .1 0 0 1 0 1 1 0 0 Truncating the 1 in the 28th position gives 00101100. Since the leading bit of this number is a 0, the answer is positive. Converting back to decimal form gives $00101100 → 101100_2 = (32 + 8 + 4)_{10} = 44_{10}.$ So the answer is 44.