Binary Hexadecimal Octal And More Conversions And Arithmetic

Explore digital versus analog signals and systems, contrasting discrete, finite values with continuous, infinite variation, illustrated through game controllers, clocks, graphs, and time fractions.

Explore bases, from base ten to binary, octal, and hexadecimal, and learn positional notation and how to convert numbers to decimal.

Convert binary to decimal by summing powers of two corresponding to set bits, using placeholders and examples like 73, 14, 136, and 496 to verify.

Identify the MSB and LSB in binary numbers, from leftmost to rightmost, using examples like binary 1010 and the impact of leading zeros.

Explore trailing zeros and trailing ones in decimal and binary, and see how they alter numbers. Remember, leading zeros don't affect value, but leading ones do.

Leading zeros do not change a number's value in decimal or binary. Leading ones, however, change the value, as shown with 12 vs 112 or 1112.

Convert decimals to binary by multiplying the fractional part by two, tracking results and noting trailing zeros and repeating patterns, with examples like 0.12, 0.375, 0.5, and 7.25.

Learn to convert between decimal, binary, and hexadecimal (base 16) using a chart and four-bit groups, including decimal to hex and hex to decimal with the pound sign.

Convert between decimal, octal, binary, and hexadecimal through practical conversions, including decimal-to-octal, octal-to-decimal, octal-to-binary, binary-to-octal, and hexadecimal-to-octal and octal-to-hexadecimal.

Convert octal to binary and binary to octal using three-bit groups, with leading-zero padding when needed; practice converting numbers like 57 base eight and 63 base eight.

Master binary addition with a column method and carry rules, including zero and carry the one, illustrated by examples like 13 plus 19, 9 plus 1, and 3 plus 3.

Explore binary subtraction rules, including borrowing from the next column, and compare them to base-ten subtraction. Practice with examples such as 1101 minus 1.

Master binary division and review decimal division using long division steps with examples like 728 ÷ 8, 728 ÷ 2, and 312 ÷ 24 to reveal quotients and remainders.