INTEGER REPRESENTATION. [For all integer questions assume 8 bits that is, show a
ID: 3764652 • Letter: I
Question
INTEGER REPRESENTATION. [For all integer questions assume 8 bits that is, show all 8 bits]
>Express 22 decimal as an unsigned binary number.
>Express 87 decimal as a signed binary number.
>Express minus 98 decimal in 1's complement form.
>Express 37 decimal in 2's complement form.
>Express minus 37 decimal in 1's complement form.
>Using 2's complement form show the result of 17 minus 3.
>Using 2's complement form show the result of 3 minus 17.
>Besides 00000000 how else can zero be expressed in 1's complement form?
CONVERSION.
>Convert 1011001100111101000111111 to hexadecimal.
>Convert this same (#9) number to decimal.
>Convert A1B2C3 to binary.
>Convert this hex {#11) to decimal.
FLOATING POINT.
>Given that 01000101000110001110000000000000 is a 32-bit IEEE Floating Point number, convert to decimal.
>Give the 32-bit IEEE Floating Point representation of -43.265625
>What is the smallest positive number that can be represented using 32-bit IEEE Floating Point notation? [Display answer as power of 2 and in the 32 bit IEEE FP format.]
Explanation / Answer
INTEGER REPRESENTATION.
22 decimal number in unsigned binary number is 00010110
87 decimal number in signed binary number is 11010111
minus 98 decimal number is 11100010 and the 1's complement form of it is 00011101
37 decimal number is 00100101 and the 2's complement form is 11011011
minus 37 decimal number in binary form is 10100101 and the 1's complement form is 01011010
steps involved in 2's complement of 17 minus 3 .
17 decimal in binary form is 10001
3 decimal in binary form is 00011
2's complement of 3 is 11101 add this to 10001 results to 01110 with a carry .neglect the carry
steps involved in 2's complement of 3 minus 17 .
3 decimal in binary form is 00011
17 decimal in binary form is 10001
2's complement of 17 is 01111 add this to 00011 results to 10010 with out a carry .therfore the reult is a negative number i.e the 2's complement of 10010 is 01110
CONVERSION.
Convert 1011001100111101000111111 and the hexadecimal number is 1667A3F
Convert this same (#9) number to decimal.:base or radix of the given number is not given
Convert A1B2C3 to binary number is 101000011011001011000011
Convert this hex {#11) to decimal.number is 1*161 +1*160
16 + 1 =17 decimal
FLOATING POINT.
steps involved in the Given 01000101000110001110000000000000 is a 32-bit IEEE Floating Point number, convert to decimal.
If the first bit 1 then the given number is negative and if the first bit 0 then the given number is positive
The given 32 bit number is a positive number why because
sign bit is 0
Exponent is 10001010 decimal number is 138 .Therefore 138-127=+11
Mantissa is 00110001110000000000000 .Therfore the decimal is 2-3 + 2-4 + 2-8 + 2-9 + 2-10
0.125 + 0.0625 + 0.00390625 + 0.001953125 +0.0009765625
0.19433594
Therefore the decimal number is 1S * ( 1 + M ) * 2E
10 * ( 1 + 0.19433594 ) * 211
11.2446
Give the 32-bit IEEE Floating Point representation of -43.265625
given decimal is a negative number and the sign bit is 1
now convert the Exponent 43 decimal to binary 00101011
now multiply the mantissa 0.265625 *2 and result the reminder from top to bottom i.e 010001
therefore the binary number is 10010101101000100000000000000000
1 bit 8 bits 23 bits Sign bit Exponent MantissaRelated Questions
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