Write the decimal number 29.23 as an unsigned fixed point binary

Question

Write the decimal number 29.23 as an unsigned fixed point binary representation with 5 bits for the integer part and 4 bits for the fractional part. Be sure to round up, if needed, to obtain the binary representation that’s closest to the actual value.



  11101.0110

 

  11101.0101

 

  11101.0100

 

  None of these

 

  11101.0011

 

Answer 1

Write the decimal number 29.23 as an unsigned fixed point binary representation with 5 bits for the integer part and 4 bits for the fractional part. Be sure to round up, if needed, to obtain the binary representation that’s closest to the actual value.

What's given in the problem:

Decimal number: 29.23

Integer bits: 5

Fractional bits: 4

Helpful Information:

1. To convert a decimal integer to binary, repeatedly divide by 2 and record the remainders in reverse order.

1. To convert a decimal fraction to binary, repeatedly multiply by 2 and record the integer parts.

1. Rounding up means choosing the closest binary representation that is greater than or equal to the decimal value.

How to solve the problem:

1. Convert the integer and fractional parts of the decimal number to binary separately, then combine them and round up if necessary.

Step 1:

Convert the integer part to binary.

Divide 29 by 2 repeatedly and record the remainders:

29/2 = 14, remainder 1

14/2 = 7, remainder 0

7/2 = 3, remainder 1

3/2 = 1, remainder 1

1/2 = 0, remainder 1

Reading the remainders from bottom to top, 29 in binary is 11101

Step 2:

Multiply 0.23 by 2 repeatedly and record the integer parts:

0.23 x 2 = 0.46, integer part 0

0.46 x 2 = 0.92, integer part 0

0.92 x 2 = 1.84, integer part 1

0.84 x 2 = 1.68, integer part 1

The first 4 bits of the fractional part are 0011.

Step 3:

Rounding the Fractional Part:

The next multiplication: 0.68 x 2 = 1.36 bit 1, fractional part 0.36

Since his next bit is 1, we round up the las bit of the fractional part

|Adding 1 to the last bit:0011 becomes 0100.

Step 4:

Combine the integer and fractional parts:

Integer part: 11101

Fractional part: 0100

Combined fixed point binary: 11101.0100

Solution:

The fixed-point binary representation of 29.23 with 5 integer bits and 4 fractional bits,

rounded up is 11101.0100

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.

Answer 2

In order to convert the number 29.23 into a fixed point binary representation with 5 bits for the integer part and 4 bits for the fractional part, let's break it down:

The integer part "29" can be converted into binary as follows:

16 8 4 2 1

1 1 1 0 1

So, "29" in binary is "11101".

The fractional part "0.23" can be converted into binary as follows:

First, calculate each bit in the fractional part by multiplying the current value by 2 and then removing the integer part of the result.

Bit 1:

0.23 * 2 = 0.46. The integer part is 0.

New value: 0.46

Bit 2:

0.46 * 2 = 0.92. The integer part is 0.

New value: 0.92

Bit 3:

0.92 * 2 = 1.84. The integer part is 1.

New value: 0.84

Bit 4:

0.84 * 2 = 1.68. The integer part is 1.

The fractional part "0.23" in binary to four places is "0011".

So, putting it all together, the number "29.23" to the closest approximation with 5 integer bits and 4 fractional bits is "11101.0011".

So, the correct answer is:

11101.0011