Computer Architecture
Exercise #8
(Fri Sept 19 2008)
Points: 24
Name: ______
Objective & InstructionsThe objective of this exercise is to gain familiarity with number representations and conversions. Answer all questions appropriately. If you are not sure about the answer you may discuss it with your neighbor or your instructor. Note that in all of the following problems the intermediate steps are worth 3 points while the final answer is worth 1 point. Good Luck!
- Convert 3610 to octal
Conversion is performed via successive divisions by 8 and writing the remainders in a bottom up fashion as shown below:
8 / 364 / 4
3610 = 448.
- Convert 1108 to decimal.
The conversion is performed by multiplying each digit (from right to left) with increasing powers of 8 and adding them together.
1108 = (1*82) + (1*81) + (0*80)
= (1*64) + (1*8) + (0*1)
= 64 + 8 + 0
= 7210
- Convert 10F16 to decimal.
The conversion is performed by multiplying each digit (rewriting hexadecimal digits to decimal values) from right to left with increasing powers of 16 and adding them together.
10F16 = (1*162) + (0*161) + (15*160) [Note F16 = 1510]
= (1*256) + (0*16) + (15*1)
= 256 + 0 + 1
= 25710
- Convert ABC16 to binary
The conversion is performed by writing 4-bit binary representation for each hexadecimal digit as shown below. The decimal values corresponding to each hexadecimal digit is shown to aid understanding (you need not include decimal values when you do the conversions).
Hex / A16 / B16 / C16Decimal / 1010 / 1110 / 1210
Binary / 10102 / 10112 / 11002
ABC16 = 1010101111002
- Convert ABC16 to binary
This conversion is performed by grouping 4-bits at a time from right to left and writing the hexadecimal digit for each group of 4-bits.
Binary / 1102 / 10012 / 01012 / 00112Hex / 616 / 916 / 516 / 316
1101001010100112 = 695316
- Convert 100111112 to Hex
This conversion is performed by grouping 4-bits at a time from right to left and writing the hexadecimal digit for each group of 4-bits.
Binary / 10012 / 11112Decimal / 910 / 1510
Hex / 916 / F16
100111112=9F16
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