Convert the numbers as indicated: a) (452) base 10 = (?) base 2 b) (72) base 10 = (?) base 8 c) (5AC2) base 16 = (?) base 2 d) (0.65) base 10 = (?) base 2
Answers
a) (452) base 10 =(?) base 2
it mean decimal value has to be convert into binary value
2 | 452 | 0
2 | 226 | 0
2 | 113 | 1
2 | 56 | 0
2 | 28 | 0
2 | 14 | 0
2 | 7 | 1
2 | 3 | 1
2 | 1 | 1
2 | 0 |
- 111000100
- (452) base 10 =( 111000100 ) base 2
b) (72) base 10 = (?) base 8
it means decimal value has to be convert into octal value
8 | 72 | 0
8 | 9 | 1
8 | 1 | 1
8 | 0 |
- 110
- (72) base 10 = (110) base 8
c) (5AC2) base 16 = (?) base 2
it means hexadecimal value has to be convert into binary value
- A = 11
- B = 12
- C = 13
- D = 14
- E = 15
◆ for 5 binary value will be
2 | 5 | 1
2 | 2 | 0
2 | 1 | 1
2 | 0 |
- 101
◆ for A means for 11
2 | 11 | 1
2 | 5 | 1
2 | 2 | 0
2 | 1 | 1
2 | 0 |
- 1011
◆ for C means for 13
2 | 13 | 1
2 | 6 | 0
2 | 3 | 1
2 | 1 | 1
2 | 0 |
- 1101
◆ for 2 binary value will be
2 | 2 | 0
2 | 1 | 1
2 | 0 |
- 10 but it is not of four bit so it will be 0010 now, it is of four bit
- 101101111010010
- (5AC2) base 16 = (101101111010010) base 2
d) (0.65) base 10 = (?) base 2
0.65 × 2 = 1 + 0.3
0.3 × 2 = 0 + 0.6
0.6 × 2 = 1 + 0.2
0.2 × 2 = 0 + 0.4
0.4 × 2 = 0 + 0.8
0.8 × 2 = 1 + 0.6
0.6 × 2 = 1 + 0.2
0.2 × 2 = 0 + 0.4
0.4 × 2 = 0 + 0.8
0.8 × 2 = 1 + 0.6
0.6 × 2 = 1 + 0.2
0.2 × 2 = 0 + 0.4
0.4 × 2 = 0 + 0.8
0.8 × 2 = 1 + 0.6
0.6 × 2 = 1 + 0.2
0.2 × 2 = 0 + 0.4
- 0.1010011001100110
- (0.65) base 10 = ( 0.1010011001100110 ) base 2
