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Liula [17]
3 years ago
7

What is the output of the sum of 1001011 and 100011 displayed in hexadecimal?

Computers and Technology
1 answer:
N76 [4]3 years ago
3 0

Answer:

1001011_2    +   100011_2   =    6E_{hex}

Explanation:

Required

1001011_2 + 100011_2 = []_{16}

First, carry out the addition in binary

1001011_2    +   100011_2   =    1101110_2

The step is as follows (start adding from right to left):

1 + 1 = 10 --- Write 0 carry 1

1 + 1 + 1(carry) = 11 ---- Write 1 carry 1

0 + 0 + 1(carry) = 1 ---- Write 1

1 + 0 = 1 --- Write 1

0 + 0 = 0 ---- Write 0

0 + 0 = 0 ---- Write 0

1 + 1 = 10 --- Write 0 carry 1

No other number to add ; So, write 1 (the last carry)

So, we have:

1001011_2    +   100011_2   =    1101110_2

Next, convert 1101110_2 to base 10 using product rule

1101110_2 = 1 * 2^6 +1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0

1101110_2 = 64 +32 + 0 + 8 + 4 + 2 + 0

1101110_2 = 110_{10}

Lastly, convert 110_{10} to hexadecimal using division and remainder rule

110/16 \to 6\ R\ 14

6/16 \to 0\ R\ 6

Write the remainder from bottom to top;

110_{10} = 6(14)_{hex}

In hexadecimal

14 \to E

So, we have:

110_{10} = 6E_{hex}

Hence:

1001011_2    +   100011_2   =    6E_{hex}

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