Question No. 1 :
Convert the following decimal numbers into binary numbers.
a) 17.35
b) 16.42
c) 15.25
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mummasdollmuski:
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Answers
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(1)
Given Decimal Equivalent = 17.35.
Calculate the left-hand side part:
2| 17
2 | 8 - 1
2| 4 - 0
2| 2 - 0
2| 1 - 0
= > (10001)
Calculate the right-hand part:
= > 0.35 * 2 = 0.7 -------------------- 0
= > 0.7 * 2 = 1.4 ---------------------- 1
= > 0.4 * 2 = 0.8 ---------------------- 0
= > 0.8 * 2 = 1.6 --------------------- 1
= > 0.6 * 2 = 1.2 --------------------- 1
= > 0.2 * 2 = 0.4 --------------------- 0
= > 0.4 * 2 = 0.8 --------------------- 0
= > 0.8 * 2 = 1.6 --------------------- 1
= > 0.6 * 2 = 1.2 --------------------- 1
= > 0.2 * 2 = 0.4 --------------------- 0
= > 0.4 * 2 = 0.8 --------------------- 0
As the fractional part is repeating. So, We shall Stop here.
Therefore binary equivalent = (10001. 0101100).
(2) 16.42
2| 16
2| 8 - 0
2| 4 - 0
2| 2 - 0
2| 1 - 0
= > (10000).
2nd part:
= > 0.42 * 2 = 0.84 --------- 0
= > 0.84 * 2 = 1.68 --------- 1
= > 0.68 * 2 = 1.36 --------- 1
= > 0.36 * 2 = 0.72 --------- 0
= > 0.72 * 2 = 1.44 --------- 1
= > 0.44 * 2 = 0.88 --------- 0
= > 0.88 * 2 = 1.76 --------- 1
= > 0.76 * 2 = 1.52 ---------- 1
= > 0.52 * 2 = 1.04 ---------- 1
= > 0.04 * 2 = 0.08 ----------- 0
= > 0.08 * 2 = 0.16 ----------- 0
= > 0.16 * 2 = 0.32 ----------- 0
= > 0.32 * 2 = 0.64 ----------- 0
= > 0.64 * 2 = 1.28 ------------ 1
= > 0.28 * 2 = 0.54 ------------ 0
= > 0.54 * 2 = 1.08 ------------ 1
= > 0.08 * 2 = 0.16 ------------ 0
= > 0.16 * 2 = 0.32 ------------ 0
As u can see the fractional part is repeating. So we can stop this.
Therefore the binary equivalent = (10000.011010111000010100).
(3) 15.25
1st part:
2| 15
2| 7 - 1
2| 3 - 1
2| 1 - 1
= > (1111).
2nd part:
= > 0.25 * 2 = 0.50 ------------------ 0
= > 0.50 * 2 = 1.00 -------------------- 1
Therefore the binary equivalent = (1111.01).
Hope this helps!
Given Decimal Equivalent = 17.35.
Calculate the left-hand side part:
2| 17
2 | 8 - 1
2| 4 - 0
2| 2 - 0
2| 1 - 0
= > (10001)
Calculate the right-hand part:
= > 0.35 * 2 = 0.7 -------------------- 0
= > 0.7 * 2 = 1.4 ---------------------- 1
= > 0.4 * 2 = 0.8 ---------------------- 0
= > 0.8 * 2 = 1.6 --------------------- 1
= > 0.6 * 2 = 1.2 --------------------- 1
= > 0.2 * 2 = 0.4 --------------------- 0
= > 0.4 * 2 = 0.8 --------------------- 0
= > 0.8 * 2 = 1.6 --------------------- 1
= > 0.6 * 2 = 1.2 --------------------- 1
= > 0.2 * 2 = 0.4 --------------------- 0
= > 0.4 * 2 = 0.8 --------------------- 0
As the fractional part is repeating. So, We shall Stop here.
Therefore binary equivalent = (10001. 0101100).
(2) 16.42
2| 16
2| 8 - 0
2| 4 - 0
2| 2 - 0
2| 1 - 0
= > (10000).
2nd part:
= > 0.42 * 2 = 0.84 --------- 0
= > 0.84 * 2 = 1.68 --------- 1
= > 0.68 * 2 = 1.36 --------- 1
= > 0.36 * 2 = 0.72 --------- 0
= > 0.72 * 2 = 1.44 --------- 1
= > 0.44 * 2 = 0.88 --------- 0
= > 0.88 * 2 = 1.76 --------- 1
= > 0.76 * 2 = 1.52 ---------- 1
= > 0.52 * 2 = 1.04 ---------- 1
= > 0.04 * 2 = 0.08 ----------- 0
= > 0.08 * 2 = 0.16 ----------- 0
= > 0.16 * 2 = 0.32 ----------- 0
= > 0.32 * 2 = 0.64 ----------- 0
= > 0.64 * 2 = 1.28 ------------ 1
= > 0.28 * 2 = 0.54 ------------ 0
= > 0.54 * 2 = 1.08 ------------ 1
= > 0.08 * 2 = 0.16 ------------ 0
= > 0.16 * 2 = 0.32 ------------ 0
As u can see the fractional part is repeating. So we can stop this.
Therefore the binary equivalent = (10000.011010111000010100).
(3) 15.25
1st part:
2| 15
2| 7 - 1
2| 3 - 1
2| 1 - 1
= > (1111).
2nd part:
= > 0.25 * 2 = 0.50 ------------------ 0
= > 0.50 * 2 = 1.00 -------------------- 1
Therefore the binary equivalent = (1111.01).
Hope this helps!
welcome!
great Bhaiya owsm ✌☺
Actually, if the same fractional part is repeating again again, we need to stop it after 5 to 6 digits.. I have continued 0.8 thrice, Its not mandatory..ur wish..U can stop it at the 2nd time also..Because we know that it will be continuing.
Welcome bro!
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