2. (111000110010)₂ conversion base2 to base8 conversion
Equivalent value list
Binary to octal→
binary Octal
base2(binary)= 111000110010
base8(octal)= 7062 oct
000 0
So, (111000110010)₂=(7062)₈
001 1
binary to decimal→
Base8(octal)= 7062 010 2
= 7*8³+0*8²+6*8¹+2*8°
011 3
= 3634 dec
So, (111000110010)₂=(3634)₁₀
100 4
binary to hexadecimal →
101 5
remainder
3634/16= 227 2 in hexadecimal form 110 6
227/16 = 14 3 in hexademal form
14/16 = 0 14=E in hexadecimal form 111 7
So,(111000110010)₂=(E32)₁₆
3. (70642)₈ conversion
Octal to decimal→
Oct= 76042 = 7*8´+6*8³+0*8²+4*8¹+2*8° = 31778 dec
So, (76042)₈= (31778)₁₀
Decimal
Operation Quotient Remainder Binary Result
Number
octal to binary→ 31778 ÷2= 15889 0 0
15889 ÷2= 7944 1 10
7944 ÷2= 3972 0 010
3972 ÷2= 1986 0 0010
1986 ÷2= 993 0 00010
993 ÷2= 496 1 100010
496 ÷2= 248 0 0100010
248 ÷2= 124 0 00100010
124 ÷2= 62 0 000100010
62 ÷2= 31 0 0000100010
31 ÷2= 15 1 10000100010
15 ÷2= 7 1 110000100010
7 ÷2= 3 1 1110000100010
3 ÷2= 1 1 11110000100010
1 ÷2= 0 1 111110000100010
4. Octal to hexadecimal→
(76042)₈= (31778)₁₀
Decimal operation quotient remainder
number
31778 ÷16 = 1986 2
1986 ÷16= 124 2
124 ÷16 = 7 12=C
7 ÷16= 0 7
0 Done.
So,
(76042)₈=(7C22)₁₆
5. (786)₁₀ conversion
Decimal to binary→
Decimal operation quotient remainder Binary result
number
786 ÷2= 393 0 0
393 ÷2= 196 1 10
196 ÷2= 98 0 010
98 ÷2= 49 0 0010
49 ÷2= 24 1 10010
24 ÷2= 12 0 010010
12 ÷2= 6 0 0010010
6 ÷2= 3 0 00010010
3 ÷2= 1 1 100010010
1 ÷2= 0 1 1100010010
So, (786)₁₀=(1100010010)₂
6. Decimal to octal→
Decimal Octal
Operation Quotient Remainder
Number Result
786 ÷8= 98 2 2
98 ÷8= 12 2 22
12 ÷8= 1 4 422
1 ÷8= 0 1 1422
0 done.
So, (786)₁₀ = (1422)₈
Decimal to hexadecimal→
Decimal Hexadecimal
Operation Quotient Remainder
Number Result
786 ÷ 16 = 49 2 2
49 ÷ 16 = 3 1 12
3 ÷ 16 = 0 3 312=3C
0 done.
So, (786)₁₀= (312)₁₆ =(3C)₁₆
7. FA09 conversion
Hexa-decimal value list:
Hexa-dec to decimal→
FA09 hexadecimal: Hexa
0 1 2 3 4 5 6 7
decimal:
= ((F)*163) + ((A)*162) + (0*161) + (9*160)
= (15*163) + (10*162) + (0* 161) + (9*160) Decimal: 0 1 2 3 4 5 6 7
= (15* 4096) + (10* 256) + (0* 16) + (9*1) Hexa
8 9 A B C D E F
= 61440+ 2560 + 0+9 decimal:
= 64009 decimal Decimal: 8 9 10 11 12 13 14 15
Hexadecimal to octal→
(FA09)₁₆=(64009)₈
Decimal
Operation Quotient Remainder octal Result
Number
64009 ÷8= 8001 1 1
8001 ÷8= 1000 1 11
1000 ÷8= 125 0 011
125 ÷8= 15 5 5011
15 ÷8= 1 7 75011
1 ÷8= 0 1 175011
So, (FA09)₁₆ =(175011)₈
8. hexadecimal digit to obtain the equivalent
Hexadecimal to binary→
group of four binary digits list:
Hexa
F A 0 9 Hexa
decimal= 0 1 2 3 4 5 6 7
decimal:
Binary= 1111 1010 0000 1001
= 1111101000001001 binary
0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1
Binary:
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
So,
(FA09)₁₆=(111101000001001)₂ Hexa
8 9 A B C DE F
decimal:
1 1 1 1 1 1 1 1
0 0 0 0 1 1 1 1
Binary:
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
