# Binary to Decimal Conversion Based on New Paper 1 Syllabus for 2021

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## 1՚s & 2՚s Complement

### 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