written 2.3 years ago by | modified 2.2 years ago by |

**Subject :** Structured Programming Approach

**Title :** Introduction to Computer, Algorithm and Flowchart

**Marks :** 4M

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Convert 0010 0100 0010 1101 from base 2 to decimal. Convert 134 from base 10 to hexadecimal. Write steps to conversion.

written 2.3 years ago by | modified 2.2 years ago by |

**Subject :** Structured Programming Approach

**Title :** Introduction to Computer, Algorithm and Flowchart

**Marks :** 4M

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written 2.2 years ago by |

**Given:**

1) $(0010 \ 0100 \ 0010 \ 1101)_2 = (?)_{10}$

2 $(134)_{10} = (?)_{16}$

**1) To Convert Base 2 to decimal:**

$(0010 \ 0100 \ 0010 \ 1101)_2 = (?)_{10}$

- Multiply the binary digits (bits) with powers of 2 according to their positional weight.
- The position of the first bit (going from right to left) is 0 and it keeps on incrementing as you go towards left for every bit.
$0*2^{15}+0*2^{14}+1*2^{13}+0*2^{12}+0*2^{11}+1*2^{10}+0*2^9+0*2^8+0*2^7+0*2^6+1*2^5+0*2^4+1*2^3+1*2^2+0*2^1+1*2^0$

$=0+0+8192+0+0+1024+0+0+0+0+32+0+8+4+1$

$=9261$

$(0010 0100 0010 1101)_2 = (9261)_{10}$

**2) To Convert Decimal to Hexadecimal:**

$(134)_{10} = (?)_{16}$

- Divide the decimal number by 16.
- Write down the remainder (in hexadecimal).
- Divide the result again by 16. Treat the division as an integer division.
- Repeat step 2 and 3 until result is 0.
- The hexadecimal value is digit sequence of the reminders from last to first.

$(134)_{10} = (86)_{16}$

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