Signed Magnitude Binary to Decimal Converter

Signed Magnitude Binary to Decimal Converter

FAQs

To convert a signed magnitude binary number to decimal, you can follow these steps:

1. Determine the sign of the number based on the leftmost (most significant) bit:
   • If the leftmost bit is ‘0’, the number is positive.
   • If the leftmost bit is ‘1’, the number is negative.
2. Convert the magnitude (the remaining bits, excluding the sign bit) from binary to decimal. You can use the standard binary-to-decimal conversion method.
3. If the number is negative (sign bit is ‘1’), make the magnitude negative by adding a negative sign in front of it.

Here are some examples:

Example 1: Convert the signed magnitude binary number “0101” to decimal:

1. The leftmost bit is ‘0’, indicating a positive number.
2. The magnitude is “101” in binary, which is 5 in decimal.
3. Since the sign bit is ‘0’, the decimal representation is positive 5.

Example 2: Convert the signed magnitude binary number “1101” to decimal:

1. The leftmost bit is ‘1’, indicating a negative number.
2. The magnitude is “101” in binary, which is 5 in decimal.
3. Since the sign bit is ‘1’, the decimal representation is negative 5.

Example 3: Convert the signed magnitude binary number “11100” to decimal:

1. The leftmost bit is ‘1’, indicating a negative number.
2. The magnitude is “1100” in binary, which is 12 in decimal.
3. Since the sign bit is ‘1’, the decimal representation is negative 12.

The key is to recognize the sign bit and handle it accordingly when converting from signed magnitude binary to decimal.