Final answer:
The smallest 32-bit binary number is 0 for unsigned representation, -2147483648 for two's complement, and -2147483647 for sign/magnitude.
Step-by-step explanation:
The smallest (most negative) 32-bit binary numbers that can be represented in different number systems are as follows:
(a) Unsigned numbers: The smallest unsigned 32-bit binary number is 00000000 00000000 00000000 00000000, which represents 0 in decimal. There are no negative numbers in unsigned representation.
(b) Two's complement numbers: The smallest two's complement 32-bit binary number is 10000000 00000000 00000000 00000000, which represents -2147483648 in decimal.
(c) Sign/magnitude numbers: The smallest sign/magnitude 32-bit binary number is also 10000000 00000000 00000000 00000000, representing -2147483647 in decimal (considering the most significant bit is used for the sign).