Question

5. What is the decimal equivalent of the largest binary integer that can be obtained with

a) 11 bits unsigned signed

b) 25 bits? unsigned signed

6. Perform the following conversion by using base 2 instead of base 10 as the intermediate base for the conversion:

a) (673.6)8 to hexadecimal

b) (E7C.B)16 to octal

Answer 1

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Straight to the question..

5)

The decimal equivalent of the largest binary integer that can be obtained with

For unsigned numbers:

The general formula is (2^n)-1

11 bits : (2^11)-1 = 2047

25 bits : (2^25)-1 = 33554431

For signed numbers:

The general formula is (2^n-1)-1

11 bits: (2^11-1)-1 = (2^10)-1 = 1023

25 bits: (2^25-1)-1 = (2^24)-1 = 16777215

6)

Conversion by using base 2 instead of base 10 as the intermediate base:

a) (673.6)8 to hexadecimal

is (1BB.C)16

(673.6)₈ = 6∙8²+7∙8¹+3∙8⁰+6∙8^-1 = 384+56+3+0.75 = (443.75)₁₀

Converting (443.75)₁₀ in Hexadecimal system here so:

Whole part of a number is obtained by dividing on the basis new

443	16
-432	27	16
11=B	-16	1
	11=B

Then (443)₁₀ = (1BB)₁₆

The fractional part of number is found by multiplying on the basis new

	0	.75
	.	16
	12=C	0

ie., (0.75)₁₀ = (0.C)₁₆

Add up together whole and fractional part here so:

(1BB)₁₆ + (0.C)₁₆ = (1BB.C)₁₆

Result of converting:
(673.6)₈ = (1BB.C)₁₆

b) (E7C.B)₁₆ to octal

is (7174.54)₈

(E7C.B)₁₆ = 14∙16²+7∙16¹+12∙16⁰+11∙16^-1 = 3584+112+12+0.6875 = (3708.6875)₁₀

Converting (3708.6875)₁₀ in Octal system here so:

Whole part of a number is obtained by dividing on the basis new

The direction of gaze is right to left side

3708	8
-3704	463	8
4	-456	57	8
	7	-56	7
		1

Then:(3708)₁₀ = (7174)₈

The fractional part of number is found by multiplying on the basis new

The direction of gaze is up to down side

	0	.6875
	.	8
	5	5
		8
	4	0

i.e., (0.6875)₁₀ = (0.54)₈

Add up together whole and fractional part here so:

(7174)₈ +( 0.54)₈ = (7174.54)₈

Result of converting:
(E7C.B)₁₆ = (7174.54)8

Hope you got your point....

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