Perform each of the following conversions ABC16 10 ABC16 8

Perform each of the following conversions: (ABC)_16 = (______)_10 (ABC)_16 = (______)_8 (ABC)_16 = (______)_BCD (ABC)_16 = (______)_2 (ABC)_16 = (______)_7

Solution

1.

(a) (ABC)₁₆ = ( )₁₀

The decimal value of A = 10, B= 11, C = 12

(ABC)₁₆ = 12*16⁰ + 11*16¹ + 10*16²

(ABC)₁₆ = 12+176+2560

(ABC)₁₆ = (2748)₁₀

(b) (ABC)₁₆ = ( )₈

To convert it into octal ,first convert into binary.

The decimal value of A = 10, B= 11, C = 12

The binary value of A = 1010, B= 1011, C = 1100

(ABC)₁₆ = (101010111100)₂

Now divide those numbers into 3 bits and you get 5=101, 2=010, 7=111, 4=100

So, (ABC)₁₆ = (5274)₈

(c) (ABC)₁₆ = ( )_BCD

(ABC)₁₆ = (0010011101001000 )_BCD

(d) (ABC)₁₆ = ( )₂

The decimal value of A = 10, B= 11, C = 12

The binary value of A = 1010, B= 1011, C = 1100

(ABC)₁₆ = (101010111100)₂

(e) (ABC)₁₆ = ( )₇

(ABC)₁₆ = (11004 )₇