Question

Convert the following 2's complement binary numbers to decimal

a)0110
b)1101
c)01101111
d)1101101100011100
e)1001110000000101

Answer 1

To convert 2's complement binary numbers to decimal, determine if the number is positive or negative, then directly convert if positive or invert all bits, add 1, and convert if negative. The provided numbers convert to 6, -3, 111, -13812, and -25979, respectively.

Step-by-step explanation:

Converting 2's Complement Binary Numbers to Decimal:

To convert 2's complement binary numbers to decimal, follow these steps:

1. Check the leftmost bit (sign bit). If it's 0, the number is positive; if it's 1, the number is negative.
2. If the number is positive, convert it to decimal normally.
3. If the number is negative, invert all the bits and add 1 to get the magnitude. Then, convert to decimal and add a negative sign.

Applying these steps:

• a) 0110: Positive, so directly convert to decimal: 6.
• b) 1101: Negative, so invert (0010), add 1 (0011), convert to decimal: -3.
• c) 01101111: Positive, so directly convert to decimal: 111.
• d) 1101101100011100: Negative, so invert and add 1 (0010010011100011 + 1 = 0010010011100100), convert to decimal: -13812.
• e) 1001110000000101: Negative, so invert and add 1 (0110001111111010 + 1 = 0110001111111011), convert to decimal: -25979.