2. 1. Convert to hexadecimal and then to binary: (a) 757.2510 (b) 1063.510

Question

logic question

Answer 1

The decimal fractions have no exact equivalent in hexadecimal or binary so I'll provide the same number of hexadecimal places as there are decimal places. That means there will be 4 times as many binary places as there are hexadecimal places.

a) Let's deal with the decimal fraction first. There are 4 decimal places so we'll get 4 hexadecimal places' accuracy. This means working out 16⁴=65536₁₀. We have to convert 0.251 so we need 65536×0.251=16450₁₀ approx. This has to be converted to hex: 16450=4×4096+4×16+2=4042₁₆. The hex fraction is 0.4042. 757=2×256+15×16+5=2F5₁₆. So 757.2510=2F5.4042₁₆ approx. In binary this is:

1011110101.0100000001000010.

b) 0.510×16³=2089₁₀ approx=8×256+2×16+9=829₁₆. 0.510=0.829₁₆. 1063=4×256+2×16+7=427₁₆. So 1063.510=427.829₁₆. Binary is 10000100111.100000101001.