Consider a modified version of the IEEE754 single-precision floating-point format as depicted in the figure below.

The floating-point format consists of the following fields:

• S (Sign-bit): a 1-bit field that equals 1 for negative numbers and 0 for positive numbers
• Integer: a 16-bit field that represents the integer portion (digits before the decimal dot) of the floating-point number as a 4221 Binary Coded Decimal (BCD) code. The 4221 BCD code represents an integer (in base 10) by converting each decimal digit into a 4-bit binary code such that:
  • the MSB (bit 3) represents the value              : 2² = 4 
  • the next bit (bit 2) represents the value         : 2¹ = 2
  • the next bit (bit 1) also represents the value : 2¹ = 2
  • the LSB (bit 0) represents the value                : 2⁰ = 1
  • For example: 
    • the integer 7 is represented using 4-bits as 1011 = 4 (MSB) + 0 + 2 + 1 (LSB)
    • the integer 23 is represented using 8-bits as 0010 0011 where the first 4 binary digits represent the number 2 (in base 10) and the last 4 binary digits represent the number 3 (in base 10)
• Fraction: a 15-bit field that represents the fractional portion (digits after the decimal dot) of the floating point number such the MSB represents 2^-1 and the LSB represents 2^-15

Represent the number -5789.125 in 32-bits based on the floating-point standard described above. Further, explain how this format changes the range of floating-point numbers that can be represented as compared to the IEEE754 single-precision format.