2
1. You shift the decimal point as far as you can to the right and then you convert the binary into a decimal by calculating its columns values i.e 1,2,4,8,16,32,64. Once you have the conversion of the binary to decimal you then divide it by 2 ^how many places you shifted decimal point. 2. You take the decimal fraction and multiply it by 2 and then take the number on the left of the decimal point which can only be either a 1 or 0 then repeat with what you have left after taking either the 1 or 0 of the left side of the decimal point. 3. An advantage of using the float point system is that when using the fixed point numbers when we want to represent either small or very large fractions we need to use a lot of bits and even when we have a lot of bits we cant represent very large numbers. Disadvantage is that the language works with floats and doubles which isn’t very precise , and another alternative is working with variable bits to represent real numbers but this would make it difficult for a machine to process. 4. The IEEE standard has a 32-bit single precision (float) and a 64-bit double precision, for binary floating-point numbers.

Workshop 7 Ict

  • Upload
    jaclyn

  • View
    217

  • Download
    0

Embed Size (px)

DESCRIPTION

solutions for workshop

Citation preview

1.You shift the decimal point as far as you can to the right and then you convert the binary into a decimal by calculating its columns values i.e 1,2,4,8,16,32,64. Once you have the conversion of the binary to decimal you then divide it by 2 ^how many places you shifted decimal point.

2.You take the decimal fraction and multiply it by 2 and then take the number on the left of the decimal point which can only be either a 1 or 0 then repeat with what you have left after taking either the 1 or 0 of the left side of the decimal point.

3.An advantage of using the float point system is that when using the fixed point numbers when we want to represent either small or very large fractions we need to use a lot of bits and even when we have a lot of bits we cant represent very large numbers.Disadvantage is that the language works with floats and doubles which isnt very precise , and another alternative is working with variable bits to represent real numbers but this would make it difficult for a machine to process.

4. The IEEE standard has a 32-bit single precision (float) and a 64-bit double precision, for binary floating-point numbers.A 32-bit single precision binary floating point number is divided into 8 bit exponent 24 bit mantissa and 1 bit sign of mantissa

When in normalized form in binary you can remove the number on the left side of the decimal point, which will only be a 1 and save a bit so you can use more bits.

5.Zero acts as a no data filler to get the 23 bits you need and also in the 32-bit IEEE format it is the start of the binary number which is the sign and is always positive.