Computers and Technology, 28.01.2020 00:31 ckenyewildon

2) show the decimal equivalent of each of the numbers if they are interpreted as (4 answers): 11001101 01101001 a. unsigned binary b. signed binary

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Answer from: cedavenport1277

11001101 (as unsigned binary) is 205 in decimal

11001101 (as signed binary) is -51 in decimal

01101001 (as unsigned binary) is 105 in decimal

01101001 (as signed binary) is still 105 in decimal.

Explanation:

a. 11001101

1 => Treating as unsigned binary

Since the number is unsigned, the usual direct conversion to decimal is sufficient. i.e

11001101 = 1 x $2^{7}$ + 1 x $2^{6}$ + 0 x $2^{5}$ + 0 x $2^{4}$ + 1 x $2^{3}$ + 1 x $2^{2}$ + 0 x $2^{1}$ + 1 x $2^{0}$

11001101 = 128 + 64 + 0 + 0 + 8 + 4 + 0 + 1

11001101 = 205 (in decimal)

Therefore 11001101 (as unsigned binary) is 205 in decimal

2 => Treating as signed binary

Signed binary using 2's complements dictates that the most significant bit (leftmost bit) in a binary number represents the sign of the bit. If the most significant bit is 0, then the number is positive. If it is 1, the number is negative.

Since the most significant bit of the number (11001101) is 1, then the number is negative.

Therefore to convert it to its decimal counterpart;

i. flip all its bits by changing all 1s to 0s and all 0s to 1s as follows

=> 11001101 = 00110010

ii. add 1 to the result above as follows

=> 00110010 + 1 = 00110011

iii. now convert the result to the decimal representation as follows

00110011 = 0 x $2^{7}$ + 0 x $2^{6}$ + 1 x $2^{5}$ + 1 x $2^{4}$ + 0 x $2^{3}$ + 0 x $2^{2}$ + 1 x $2^{1}$ + 1 x $2^{0}$

00110011 = 0 + 0 + 32 + 16 + 0 + 0 + 2 + 1

00110011 = 51 (in decimal)

Therefore, 11001101 (as signed binary) is -51 in decimal

b. 01101001

1 => Treating as unsigned binary

Since the number is unsigned, the usual direct conversion to decimal is sufficient. i.e

01101001 = 0 x $2^{7}$ + 1 x $2^{6}$ + 1 x $2^{5}$ + 0 x $2^{4}$ + 1 x $2^{3}$ + 0 x $2^{2}$ + 0 x $2^{1}$ + 1 x $2^{0}$

01101001 = 0 + 64 + 32 + 0 + 8 + 0 + 0 + 1

01101001 = 105 (in decimal)

Therefore 01101001 (as unsigned binary) is 105 in decimal

2 => Treating as signed binary

Since the most significant bit of the number (01101001) is 0, then the number is positive and the usual conversion to decimal will suffice. i.e

01101001 = 0 x $2^{7}$ + 1 x $2^{6}$ + 1 x $2^{5}$ + 0 x $2^{4}$ + 1 x $2^{3}$ + 0 x $2^{2}$ + 0 x $2^{1}$ + 1 x $2^{0}$

01101001 = 0 + 64 + 32 + 0 + 8 + 0 + 0 + 1

01101001 = 105 (in decimal)

Therefore 01101001 (as signed binary) is still 105 in decimal.

Note: A positive binary number will have the same value (in decimal) whether it is treated as signed or unsigned.

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