Conversion-and-Binary-Calculation-Number-system

1. Convert the following Binary Numbers into decimal Numbers.

a.1101

$1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $1101_{2} = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$

$1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$ $1101_{2} = 8 + 4 + 0 + 1$

$1101_{2} = 13_{10}$ $1101_{2} = 13_{10}$ $1101_{2} = 13_{10}$ $1101_{2} = 13_{10}$

b.11101

$11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$ $11101_{2} = (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$

$11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$ $11101_{2} = 16 + 8 + 4 + 0 + 1$

$11101_{2} = 29_{10}$ $11101_{2} = 29_{10}$ $11101_{2} = 29_{10}$ $11101_{2} = 29_{10}$

c. 10101

$10101_{2} = (1 \times 2^{4}) + (0 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0})$

$10101_{2} = 16 + 0 + 4 + 0 + 1$

$10101_{2} = 21_{10}$

D. 1011

1011_{2} = (1 \times 2^{3}) + (0 \times 2^{2}) + (1 \times 2^{1}) + (1 \times 2^{0})

1011_{2} = 8 + 0 + 2 + 1

1011_{2} = 11_{10}

E. 1010

1011_{2} = (1 \times 2^{3}) + (0 \times 2^{2}) + (1 \times 2^{1}) + (1 \times 2^{0})

1011_{2} = 8 + 0 + 2 + 1

1011_{2} = 11_{10}

{F. 10011}

${(10011)₂ = (1 \times 2⁴) + (0 \times 2³) + (0 \times 2²) + (1 \times 2¹) + (1 \times 2⁰)}$
${(10011)₂ = (19)₁₀}$

{G. 11011}

${(11011)₂ = (1 \times 2⁴) + (1 \times 2³) + (0 \times 2²) + (1 \times 2¹) + (1 \times 2⁰)}$
${(11011)₂ = (27)₁₀}$

2. Convert the following decimal Numbers into Binary Numbers.

a. 27

2	27
2	13	1
2	6	1
2	3	0
2	1	1
2	0	1

2710=110112

B. 65

2	65
2	32	1
2	16	0
2	8	0
2	4	0
2	2	0
2	1	0
2	0	1

6510 = 10000012

C. 90

2	90
2	45	0
2	22	1
2	11	0
2	5	1
2	2	1
2	1	0
2	0	1

9010 = 10110102

D. 122

2	122
2	61	0
2	30	1
2	15	0
2	7	1
2	3	1
2	1	1
2	0	1

12210 = 111101

E. 164

2	164
2	82	0
2	41	0
2	20	1
2	10	0
2	5	0
2	2	1
2	1	0
2	0	1

16410 = 101001002

F.125

2	125
2	62	1
2	31	0
2	15	1
2	7	1
2	3	1
2	1	1
2	0	1

12510 = 11111012

G. 255

2	255
2	127	1
2	63	1
2	31	1
2	15	1
2	7	1
2	3	1
2	1	1
2	0	1

25510 = 111111112

H. 456

2	456
2	228	0
2	114	0
2	57	0
2	28	1
2	14	0
2	7	0
2	3	1
2	1	1
2	0	1

45610 = 1110010002

3.Convert the following octal numbers into decimal Numbers.

A.245

$245_{8} = (2 \times 8^{2}) + (4 \times 8^{1}) + (5 \times 8^{0})$

$245_{8} = 128 + 32 + 5$

$245_{8} = 165_{10}$

B. 324

$324_{8} = (3 \times 8^{2}) + (2 \times 8^{1}) + (4 \times 8^{0})$

$324_{8} = 192 + 16 + 4$

$324_{8} = 212_{10}$

C. 650

$650_{8} = (6 \times 8^{2}) + (5 \times 8^{1}) + (0 \times 8^{0})$

$650_{8} = 384 + 40 + 0$

$650_{8} = 424_{10}$

D. 1027

$1027_{8} = (1 \times 8^{3}) + (0 \times 8^{2}) + (2 \times 8^{1}) + (7 \times 8^{0})$

$1027_{8} = 512 + 0 + 16 + 7$

$1027_{8} = 535_{10}$

E. 3654

$3654_{8} = (3 \times 8^{3}) + (6 \times 8^{2}) + (5 \times 8^{1}) + (4 \times 8^{0})$

$3654_{8} = 1536 + 384 + 40 + 4$

$3654_{8} = 1964_{10}$

F. 1456

$1456_{8} = (1 \times 8^{3}) + (4 \times 8^{2}) + (5 \times 8^{1}) + (6 \times 8^{0})$

$1456_{8} = 512 + 256 + 40 + 6$

$1456_{8} = 814_{10}$

G. 437

$437_{8} = (4 \times 8^{2}) + (3 \times 8^{1}) + (7 \times 8^{0})$

$437_{8} = 256 + 24 + 7$

$437_{8} = 287_{10}$

4. Convert the following decimal numbers into octal numbers.

A. 809

8	809
8	101	1
8	12	5
8	1	4
8	0	1

809_{10} = 1451_{8}

B. 867

8	867
8	108	3
8	13	4
8	1	5
8	0	1

$867_{10} = 1543_{8}$

C. 97

8	97
8	12	1
8	1	4
8	0	1

97_{10} = 141_{8}

D.345

8	345
8	43	1
8	5	3
8	0	5

$345_{10} = 531_{8}$

E. 985

8	985
8	123	1
8	15	3
8	1	7
8	0	1

$985_{10} = 1731_{8}$

F. 256

8	256
8	32	0
8	4	0
8	0	4

$256_{10} = 400_{8}$

G. 127

8	127
8	15	7
8	1	7
8	0	1

$127_{10} = 177_{8}$

5. Convert the following Hexadecimal numbers to decimal numbers.

A. 3FA

$3 FA_{16} = (3 \times 16^{2}) + (15\times 16^{1}) + (10 \times 16^{0})$

$3 FA_{16} = 768 + 240 + 10$

$3 FA_{16} = 1018_{10}$

B. A0B

$A 0 B_{16} = (10 \times 16^{2}) + (0 \times 16^{1}) + (11 \times 16^{0})$

$A 0 B_{16} = 2560 + 0 + 11$

$A 0 B_{16} = 257110$

C. 4DF

$4 D F_{16} = (4 \times 16^{2}) + (13 \times 16^{1}) + (15 \times 16^{0})$

$4 D F_{16} = 1024 + 208 + 15$
$4 D F_{16} = 1247_{10}$

D. 9C3

$9 C 3_{16} = (9 \times 16^{2}) + (12 \times 16^{1}) + (3 \times 16^{0})$

$9 C 3_{16} = 2304 + 192 + 3$

$9 C 3_{16} = 2499_{10}$

E. 154

$154_{16} = (1 \times 16^{2}) + (5 \times 16^{1}) + (4 \times 16^{0})$

$154_{16} = 256 + 80 + 4$

$154_{16} = 340_{10}$

F. 10E

$10 E_{16} = (1 \times 16^{2}) + (0 \times 16^{1}) + (14 \times 16^{0})$

$10 E_{16} = 256 + 0 + 14$

10 E_{16} = 270_{10}

G. 2785

$2785_{16} = (2 \times 16^{3}) + (7 \times 16^{2}) + (8 \times 16^{1}) + (5 \times 16^{0})$

$2785_{16} = 8192 + 1792 + 128 + 5$

$2785_{16} = 10117_{10}$

6. Convert the following Decimal Numbers into hexadecimal numbers.

A. 1021

16	1021
16	63	13
16	3	15
16	0	3

$1021_{10} = 3 FD_{16}$

B. 3042

16	3042
16	190	2
16	11	14
16	0	11

$3042_{10} = BE 2_{16}$

C. 2365

16	2365
16	147	13
16	9	3
16	0	9

$2365_{10} = 93 {D16}$

D. 2456

16	2456
16	153	8
16	9	9
16	0	9

$2456_{10} = 998_{16}$

E. 410

16	410
16	25	10
16	1	9
16	0	1

$410_{10} = 19 A_{16}$

F. 785

16	785
16	49	1
16	3	1
16	0	3

$785_{10} = 311_{16}$

G . 154

16	154
16	9	10
16	0	9

$154_{10} = 9 A_{16}$

7. Convert the following binary numbers into octal numbers.

A. 1111101

001111101
175

$1111101_{2} = 175_{8}$

B. 10110110

010110110
266

$10110110_{2} = 266_{8}$

C.10000101

010000101
205

$10000101_{2} = 205_{8}$

D. 11101110

011101110
356

$11101110_{2} = 356_{8}$

E. 10110111

010110111
267

$10110111_{2} = 267_{8}$

8. Convert the following octal into Binary numbers.

A. 654

654
110101100

$654_{8} = 110101100_{2}$

B.743

743
111100011

$743_{8} = 111100011_{2}$

C.457

457
100101111

$457_{8} = 100101111_{2}$

D. 507

507
101000111

$507_{8} = 101000111_{2}$

E. 554

554
101101100

$554_{8} = 101101100_{2}$

9. Converts the following Binary numbers into hexadecimal numbers.

A. 111101010

000111101010
1EA

$111101010_{2} = 1 E A_{16}$

B. 101101001

000101101001
169

$101101001_{2} = 169_{16}$

C. 1111000101

001111000101
3C5

$1111000101_{2} = 3 C 5_{16}$

D. 1011001101

001011001101
2CD

$1011001101_{2} = 2 C D_{16}$

E.1001001110

001001001110
24E

$1001001110_{2} = 24 E_{16}$

10. Converts the following hexadecimal into binary number system.

A. DDF

DDF
110111011111

$D D F_{16} = 110111011111_{2}$

B.872

872
100001110010

$872_{16} = 100001110010_{2}$

C. 39C

39C
001110011100

$39 C_{16} = 001110011100_{2}$

D. EDC

EDC
111011011100

$E D C_{16} = 111011011100_{2}$

E. A97

A97
101010010111

A 97_{16} = 101010010111_{2}

11. Convert the following as indicated.

A. a.(A24)16=(?)8

Convert Hexa Decimal number to binary
A24
101000100100

$A 24_{16} = 101000100100_{2}$

Convert Binary Number into Octal Number

101000100100
5044

$101000100100_{2} = 5044_{8}$

B. (773)8=(?)16

Convert Octal Number into Binary Number
773
111111011

$773_{8} = 111111011_{2}$

Convert Binary Number into Hex Number

000111111011
1FB

$111111011_{2} = 1 F B_{16}$

C. (D0E)16=(?)8

Convert Hexa Decimal number to binary
D0E
110100001110

$D 0 E_{16} = 110100001110_{2}$

Convert Binary Number into Octal Number
Split the binary number from left to right each group 3 bits
110100001110
6416

$110100001110_{2} = 6416_{8}$

D. (3467)16=(?)8

Convert Hexa Decimal number to binary
3467
0011010001100111

$3467_{16} = 0011010001100111_{2}$

Convert Binary Number into Octal Number

000011010001100111
032147

$0011010001100111_{2} = 32147_{8}$

E. (970)8=(?)16

F.(204)8=(?)16

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