Question

Assume each value below shows an integer in 2's complement representation in 2, 4, 8, and 16 bits length. Convert each binary number to decimal.

A.10
B.1000
C.10101110
D.1101010011111000

Answer 1

The binary numbers in 2's complement representation: A. 10 converts to -2, B. 1000 to -8, C. 10101110 to -68, and D. 1101010011111000 to -24248 in decimal form.

Step-by-step explanation:

The question involves converting binary numbers in 2's complement representation to decimal. Here's how you can do the conversions:

• A. 10 is a 2-bit number. Since the leftmost bit is 1, it represents a negative number. The value is -21 + 20 which is -2 + 0 = -2 in decimal.
• B. 1000 is a 4-bit number. Again, the leftmost bit is 1, so it's negative. The value is -23 + 0+ 0+ 0 = -8 in decimal.
• C. 10101110 is an 8-bit number. The leftmost bit is 1, indicating it's negative. The value is -27 + 0 + 25 + 24 + 23 + 22 + 0 - 20 = -128 + 32 + 16 + 8 + 4 - 1 = -68 in decimal.
• D. 1101010011111000 is a 16-bit number. The leftmost bit being 1 means it's negative. The value is -215 + 214 + 0 + 212 + 211 + 0 + 0 + 28 + 27 + 26 + 25 + 24 + 23 + 22 + 0 + 0 = -32768 + 16384 + 4096 + 2048 + 512 + 256 + 128 + 64 + 16 + 8 + 4 = -24248 in decimal.