Question

CIS360: Info Tech Hardware & Software B. (2x points) For the following binary numbers, calculate the decimal and hexadecimal equivalent. a10111001 b. 0001011012

Answer 1

Solution

a)

10111001

Convert  10111001 to decimal

To convert binary number 10111001 to decimal, follow these two steps:

Start from one's place in 10111001 : multiply ones place with 2^0, tens place with 2^1, hundreds place with 2^2 and so on from right to left

Add all the product we got from step 1 to get the decimal equivalent of 10111001.

Using the above steps, here is the work involved in the solution for converting 10111001 to decimal number (Don't forget that we start from ones place to so on...)

Decimal equivalent of "1" = 1 × 2^0 = 1
Decimal equivalent of "0" = 0 × 2^1 = 0
Decimal equivalent of "0" = 0 × 2^2 = 0
Decimal equivalent of "1" = 1 × 2^3 = 8
Decimal equivalent of "1" = 1 × 2^4 = 16
Decimal equivalent of "1" = 1 × 2^5 = 32
Decimal equivalent of "0" = 0 × 2^6 = 0
Decimal equivalent of "1" = 1 × 2^7 = 128
Decimal equivalent of "10111001" = 1+0+0+8+16+32+0+128
10111001 = 185

Here is the final answer, The binary number 10111001 converted to decimal is therefore equal to:

185

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Convert  10111001 to hexadecimal

Answer

10111001₂ = B9₁₆

divide into four bits

1011 1001

1011 is B in Hexadecimal

1001 is 9 in Hexadecimal

Therefore answer is

B9

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b)

000101101

convert 000101101 to decimal

To convert binary number 000101101 to decimal, follow these two steps:

Start from one's place in 000101101 : multiply ones place with 2^0, tens place with 2^1, hundreds place with 2^2 and so on from right to left

Add all the product we got from step 1 to get the decimal equivalent of 000101101.

Using the above steps, here is the work involved in the solution for converting 000101101 to decimal number (Don't forget that we start from ones place to so on...)

Decimal equivalent of "1" = 1 × 2^0 = 1
Decimal equivalent of "0" = 0 × 2^1 = 0
Decimal equivalent of "1" = 1 × 2^2 = 4
Decimal equivalent of "1" = 1 × 2^3 = 8
Decimal equivalent of "0" = 0 × 2^4 = 0
Decimal equivalent of "1" = 1 × 2^5 = 32
Decimal equivalent of "0" = 0 × 2^6 = 0
Decimal equivalent of "0" = 0 × 2^7 = 0
Decimal equivalent of "0" = 0 × 2^8 = 0
Decimal equivalent of "000101101" = 1+0+4+8+0+32+0+0+0
000101101 = 45

Here is the final answer, The binary number 000101101 converted to decimal is therefore equal to:

45

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convert 000101101 to hexadecimal

000101101₂ = 2D₁₆

divide into four bits

0 0010 1101

0010 is 2 in hexadecimal

1101 is D in hexadecimal

Therefore Answer is

2D₁₆

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