# Binary to Decimal Conversion Based on New Paper 1 Syllabus for 2020

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## 1’S & 2’S Complement

Watch Video Lecture on YouTube: Examrace

Converting Decimal to Binary & Binary to Decimal - 2 Simple Tricks: Computers

### Fast Speed

### Convert to Binary: 2432 (Unsigned)

Ans: 100110000000

2048, 256, 128

Check if number is even its lsb would be 0 else would be 1

### Convert to Decimal: 11011001 (Unsigned)

Ans: 11011001 = 217

2048, 256, 128

Check if number is even its lsb would be 0 else would be 1

### The Negatives!!

Signed Magnitude (5 bit machine)

1’s Complement (5 bit machine)

2’s Complement (5 bit machine)

-5 Singed magnitude- 10101, 1’s Complement: 11010, 2’s complement: 11011.

10101 signed magnitude: -5, 1’s Complement: -10, 2’s Complement -11

2’s Complement = 1’s Complement + 1

Negative numbers always have 1 in MSB!

In all numbers +ve remain the same as unsigned

### The Negatives: Signed Magnitude

-5 Singed magnitude: 10101

-15 Singed magnitude: 11111

11011: -11

### 01011: 11 the Negatives: 1’S Complement

-5 1’s Complement: 11010 (Need machine

width- guess from choices)

-15 1’s Complement: 10000 (More width would produce more 1’s)

11011: -4 (MSB is one so negative number, complement and find answer) If no 1 in MSB then simply write 11

01011: 11 (Same as unsigned)

## The Negatives: 2’S Complement

-5 2’s Complement: 11011 (Need machine width- guess from choices) (Add one to 1’s Complement only for negative numbers)

-15 2’s Complement: 10001 (More width would produce more 1’s)

11011: -5 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 11

11110: -2 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 14

01011: 11 (Same as unsigned)

### Fractions in Binary!!

### Next Class

-5 2’s Complement: 11011 (Need machine width- guess from choices) (Add one to 1’s Complement only for negative numbers)

-15 2’s Complement: 10001 (More width would produce more 1’s)

11011: -5 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 11

11110: -2 (MSB is one so negative number, -1 and then complement and find answer) If no 1 in MSB then simply write 14

01011: 11 (Same as unsigned)

-Manishika